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1.
E. Ballico 《Annali dell'Universita di Ferrara》1982,38(1):33-40
Summary Here we prove the following result. Fix integersq, τ,a’, b’, a’
i, 1≤i≤τ,a’, b’, a’
i, 1≤i≤τ; then there is an integerew such that for every integert≥w, for every algebraically closed fieldK for every smooth complete surfaceX with negative Kodaira dimension, irregularityq andK
X
2
=8(1−q)−τ, the following condition holds; ifX→S is a sequence fo τ blowing-downs which gives a relatively minimal model with ruling ρ:S→C, take as basis of the Neron Severi groupNS(X) a smooth rational curve which is the total transform of a fiber ofC, the total transform of a minimal section of ρ and the total transformD
i, 1≤i≤τ, of the exceptional curver; then for everyH andL∈Pic (X) withH ample,H (resp.L) represented by the integersa’, b’, a’
i, (resp.a’, b’, a’
i), 1≤i≤τ, in the chosen basis ofNS(X) the moduli spaceM(ZX, 2,H, L, t) of rank 2H-stable vector bundles onX with determinantL andc
2=t is generically smooth and the number, dimension and ?birational structure? of the irreducible components ofM(X, 2,H, L, t)red do not depend on the choice ofK andX. Furthermore the birational structure of these irreducible components can be loosely described in terms of the birational
structure of the components of suitableM(S, 2,H’, L’, t’)red withS a relatively minimal model ofX.
Sunto SiaX una superficie algebrica liscia completa con dimensione di Kodaira negativa e definita su un campo algebricamente chiusoK; fissiamoH eL∈Pic (X),t∈Z; siaq l’irregolarità diX e τ≔8(1−q)−K X Emphasis>2 ; siaM(X, 2,H, L, t) to schema dei moduli dei fibrati vettorialiH-stabili di rango 2 suX con determinateL ec 2=t. Si dimostra che esiste una costantew che dipende solo daq, da τ e dalla classe numerica diH e diL (ma non da char (K) o dalla classe di isomorphismo diX) tale che per ognit≥w il numero, la dimensione e ?la struttura birazionale? delle componenti irriducibili diM(X, 2,H, L, t)red non dipende dalla scelta di char (K),K eX ma solo daq, τ e dalle classi diH eL inNS(X). Inoltre la ?struttura birazionale? di queste componenti irriducibili può essere grossolanamente descritta in termini delle componenti di opportuni spazi di moduliM(S, 2,H’, L’, t’) (doveS è un modello minimale diX).相似文献
2.
In the present paper, we advance considerably the current knowledge on the topic of bifurcations of heteroclinic cycles for
smooth, meaning C
∞, parametrized families {g
t
∣t∈ℝ} of surface diffeomorphisms. We assume that a quadratic tangency q is formed at t=0 between the stable and unstable lines of two periodic points, not belonging to the same orbit, of a (uniformly hyperbolic)
horseshoe K (see an example at the Introduction) and that such lines cross each other with positive relative speed as the parameter evolves,
starting at t=0 and the point q. We also assume that, in some neighborhood W of K and of the orbit of tangency o(q), the maximal invariant set for g
0=g
t=0 is K∪o(q), where o(q) denotes the orbit of q for g
0. We then prove that, when the Hausdorff dimension HD(K) is bigger than one, but not much bigger (see (H.4) in Section 1.2 for a precise statement), then for most t, |t| small, g
t
is a non-uniformly hyperbolic horseshoe in W, and so g
t
has no attractors in W. Most t, and thus most g
t
, here means that t is taken in a set of parameter values with Lebesgue density one at t=0. 相似文献
3.
Frédéric Vanhove 《Journal of Algebraic Combinatorics》2011,34(3):357-373
The inequality of Higman for generalized quadrangles of order (s,t) with s>1 states that t≤s
2. We generalize this by proving that the intersection number c
i
of a regular near 2d-gon of order (s,t) with s>1 satisfies the tight bound c
i
≤(s
2i
−1)/(s
2−1), and we give properties in case of equality. It is known that hemisystems in generalized quadrangles meeting the Higman
bound induce strongly regular subgraphs. We also generalize this by proving that a similar subset in regular near 2d-gons meeting the bounds would induce a distance-regular graph with classical parameters (d,b,α,β)=(d,−q,−(q+1)/2,−((−q)
d
+1)/2) with q an odd prime power. 相似文献
4.
Given a graph G with characteristic polynomial ϕ(t), we consider the ML-decomposition ϕ(t) = q
1(t)q
2(t)2 ... q
m
(t)m, where each q
i
(t) is an integral polynomial and the roots of ϕ(t) with multiplicity j are exactly the roots of q
j
(t). We give an algorithm to construct the polynomials q
i
(t) and describe some relations of their coefficients with other combinatorial invariants of G. In particular, we get new bounds for the energy E(G) =
|λi| of G, where λ1, λ2, ..., λn are the eigenvalues of G (with multiplicity). Most of the results are proved for the more general situation of a Hermitian matrix whose characteristic
polynomial has integral coefficients.
This work was done during a visit of the second named author to UNAM. 相似文献
5.
Jumela F. Sarmiento 《Graphs and Combinatorics》2002,18(3):621-632
A t(v,k,λ) design is a set of v points together with a collection of its k-subsets called blocks so that t points are contained in exactly λ blocks. PG(n,q), the n-dimensional projective geometry over GF(q) is a 2(q
n
+q
n−1
+⋯+q+1,q
2+q+1, q
n−2
+ q
n−3
+⋯+q+1) design when we take its points as the points of the design and its planes as the blocks of the design. A 2(v,k,λ) design is said to be resolvable if the blocks can be partitioned as ℱ={R
1,R
2,…,R
s
}, where s=λ(v−1)/(k−1) and each R
i
consists of v/k disjoint blocks. If a resolvable design has an automorphism σ which acts as a cycle of length v on the points and ℱσ=ℱ, then the design is said to be point-cyclically resolvable. The design consisting of points and planes of PG(5,2) is shown to be point-cyclically resolvable by enumerating all inequivalent
resolutions which are invariant under a cyclic automorphism group G=〈σ〉 where σ is a cycle of length v. These resolutions are shown to be the only resolutions which admit point-transitive automorphism group.
Received: November 10, 1999 Final version received: September 18, 2000
Acknowledgments. The author would like to thank A. Munemasa for his assistance in writing computer programs on constructing projective spaces
and searching for partial spreads. Moreover, she's thankful to T. Hishida and M.␣Jimbo for helpful discussions and for verifying
the results of this paper.
Present address: Mathematics Department, Ateneo de Manila University, Loyola Heights, Quezon City 1108, Philippines. e-mail: jumela@mathsci.math.admu.edu.ph 相似文献
6.
Summary Let (X, L) be a pair consisting of a smooth, algebraic, non-ruled surfaceX and a very ample line bundleL on it. In this paper we classifyX in the casesď=2g−i, wherei=2, … 5,g is the sectional genus ofX andď is the degree of the minimal reduction
ofX. We also give good estimates of the irregularityq and the geometric genusp
g. In particular we apply our results to the caseg=7.
Riassunto Sia (X, L) la coppia formata da una superficie algebrica, liscia, non-rigataX e un fibrato di retteL molto ampio suX. In questo lavoro diamo una classificazione diX nel caso in cuiď=2g−i, dovei=2, … 5,q è il genere sezionale diX eď è il grado della riduzione minimale diX. Diamo anche delle stime dell'irregolaritàq e del genere geometricop g diX. In particolare applichiamo i nostri risultati al casoq=7.相似文献
7.
We say that n independent trajectories ξ1(t),…,ξ
n
(t) of a stochastic process ξ(t)on a metric space are asymptotically separated if, for some ɛ > 0, the distance between ξ
i
(t
i
) and ξ
j
(t
j
) is at least ɛ, for some indices i, j and for all large enough t
1,…,t
n
, with probability 1. We prove sufficient conitions for asymptotic separationin terms of the Green function and the transition
function, for a wide class of Markov processes. In particular,if ξ is the diffusion on a Riemannian manifold generated by
the Laplace operator Δ, and the heat kernel p(t, x, y) satisfies the inequality p(t, x, x) ≤ Ct
−ν/2 then n trajectories of ξ are asymptotically separated provided . Moreover, if for some α∈(0, 2)then n trajectories of ξ(α) are asymptotically separated, where ξ(α) is the α-process generated by −(−Δ)α/2.
Received: 10 June 1999 / Revised version: 20 April 2000 / Published online: 14 December 2000
RID="*"
ID="*" Supported by the EPSRC Research Fellowship B/94/AF/1782
RID="**"
ID="**" Partially supported by the EPSRC Visiting Fellowship GR/M61573 相似文献
8.
Abstract Let X be a non–hyperelliptic curve of genus g which is a double covering of a hyperelliptic curve C of genus h. In this paper, we prove that, if h≥ 3 and g≥ 4h+5, then X admits a complete, base point free g1g–2. Moreover, if h=3, this result holds under the mild condition g≥ 4h+3=15.
Keywords: Double covering of hyperelliptic curves, Pencil of degree g–2
Mathematics Subject Classification (2000:) 14H30, 14H45 相似文献
9.
Edoardo Ballico 《Annali dell'Universita di Ferrara》1985,31(1):63-70
Summary Fixr≥2,N=r(r+3)/2 andN smooth plane curvesA
1…,A
N with degA
i>-2 fori=l,…,N. Then the monodromy group for the plane curves of degreer tangent tog
iAi, gi∈PGL(3), is the full symmetric group.
Supported in part by NATO junior fellowship at M.I.T. 相似文献
Riassunto Sianor≥2,N=r(r+3)/2 eA 1…,A N curve piane lisce di grado almeno 2. Si dimostra che la monodromia per le curve piane di grador tangenti ag 1 A i,g i∈PGL(3), è il gruppo simmetrico.
Supported in part by NATO junior fellowship at M.I.T. 相似文献
10.
An upper bound estimate in the law of the iterated logarithm for Σf(n
k ω) where nk+1∫nk≧ 1 + ck
-α (α≧0) is investigated. In the case α<1/2, an upper bound had been given by Takahashi [15], and the sharpness of the bound
was proved in our previous paper [8]. In this paper it is proved that the upper bound is still valid in case α≧1/2 if some
additional condition on {n
k} is assumed. As an application, the law of the iterated logarithm is proved when {n
k} is the arrangement in increasing order of the set B(τ)={1
i
1...qτ
i
τ|i1,...,iτ∈N
0}, where τ≧ 2, N
0=NU{0}, and q
1,...,q
τ are integers greater than 1 and relatively prime to each others.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
11.
We consider amalgamated free product II1 factors M = M
1*B
M
2*B
… and use “deformation/rigidity” and “intertwining” techniques to prove that any relatively rigid von Neumann subalgebra Q ⊂ M can be unitarily conjugated into one of the M
i
’s. We apply this to the case where the M
i
’s are w-rigid II1 factors, with B equal to either C, to a Cartan subalgebra A in M
i
, or to a regular hyperfinite II1 subfactor R in M
i
, to obtain the following type of unique decomposition results, àla Bass–Serre: If M = (N
1 * CN2*C
…)
t
, for some t > 0 and some other similar inclusions of algebras C ⊂ N
i
then, after a permutation of indices, (B ⊂ M
i
) is inner conjugate to (C ⊂ N
i
)
t
, for all i. Taking B = C and , with {t
i
}
i⩾1 = S a given countable subgroup of R
+
*, we obtain continuously many non-stably isomorphic factors M with fundamental group equal to S. For B = A, we obtain a new class of factors M with unique Cartan subalgebra decomposition, with a large subclass satisfying and Out(M) abelian and calculable. Taking B = R, we get examples of factors with , Out(M) = K, for any given separable compact abelian group K. 相似文献
12.
Shu-Yu Hsu 《Mathematische Annalen》2006,334(1):153-197
Let a1,a2, . . . ,am ∈ ℝ2, 2≤f ∈ C([0,∞)), gi ∈ C([0,∞)) be such that 0≤gi(t)≤2 on [0,∞) ∀i=1, . . . ,m. For any p>1, we prove the existence and uniqueness of solutions of the equation ut=Δ(logu), u>0, in satisfying and logu(x,t)/log|x|→−f(t) as |x|→∞, logu(x,t)/log|x−ai|→−gi(t) as |x−ai|→0, uniformly on every compact subset of (0,T) for any i=1, . . . ,m under a mild assumption on u0 where We also obtain similar existence and uniqueness of solutions of the above equation in bounded smooth convex domains of ℝ2 with prescribed singularities at a finite number of points in the domain. 相似文献
13.
A sequence (z
0,z
1,z
2,, ...,z
n, z
n+1) of points fromp=z
0 toq=z
n+1 in a metric spaceX is said to besequentially equidistant ifd(z
i−1,z
i)=d(z
i,z
i+1) for 1≦i≦n. If there is path inX fromp toq (or if a certain weaker condition holds), then such a sequence exists, with all points distinct, for every choice ofn, while ifX is compact and connected, then such a sequence exists at least forn=2. An example is given of a dense connected subspaceS ofR
m
,m≧2, and an uncountable dense subsetE disjoint fromS for which there is no sequentially equidistant sequence of distinct points (n ≧ 2) inS ∪E between any two points ofE. Techniques of dimension theory are utilized in the construction of these examples, as well as in the proofs of some of the
positive results.
Supported in part by NSF Grant DMS-8701666. 相似文献
14.
Chris Pollett 《Archive for Mathematical Logic》2003,42(5):469-488
The paper establishes lower bounds on the provability of 𝒟=NP and the MRDP theorem in weak fragments of arithmetic. The
theory I
5
E
1
is shown to be unable to prove 𝒟=NP. This non-provability result is used to show that I
5
E
1
cannot prove the MRDP theorem. On the other hand it is shown that I
1
E
1
proves 𝒟 contains all predicates of the form (∀i≤|b|)P(i,x)^Q(i,x) where ^ is =, <, or ≤, and I
0
E
1
proves 𝒟 contains all predicates of the form (∀i≤b)P(i,x)=Q(i,x). Here P and Q are polynomials. A conjecture is made that 𝒟 contains NLOGTIME. However, it is shown that this conjecture would not be sufficient
to imply 𝒟=N P. Weak reductions to equality are then considered as a way of showing 𝒟=NP. It is shown that the bit-wise less than predicate,
≤2, and equality are both co-NLOGTIME complete under FDLOGTIME reductions. This is used to show that if the FDLOGTIME functions
are definable in 𝒟 then 𝒟=N P.
Received: 13 July 2001 / Revised version: 9 April 2002 /
Published online: 19 December 2002
Key words or phrases: Bounded Arithmetic – Bounded Diophantine Complexity 相似文献
15.
We prove large deviation results on the partial and random sums Sn = ∑i=1n Xi,n≥1; S(t) = ∑i=1N(t) Xi, t≥0, where {N(t);t≥0} are non-negative integer-valued random variables and {Xn;n≥1} are independent non-negative random variables with distribution, Fn, of Xn, independent of {N(t); t≥0}. Special attention is paid to the distribution of dominated variation. 相似文献
16.
Martin Cook 《Journal of Algebraic Combinatorics》2010,31(3):319-353
Let G be an adjoint simple algebraic group over an algebraically closed field of characteristic p; let Φ be the root system of G, and take t∈ℕ. Lawther has proven that the dimension of the set G
[t]={g∈G:g
t
=1} depends only on Φ and t. In particular the value is independent of the characteristic p; this was observed for t small and prime by Liebeck. Since G
[t] is clearly a disjoint union of conjugacy classes the question arises as to whether a similar result holds if we replace G
[t] by one of those classes. This paper provides a partial answer to that question. A special case of what we have proven is
the following. Take p,q to be distinct primes and G
p
and G
q
to be adjoint simple algebraic groups with the same root system and over algebraically closed fields of characteristic p and q respectively. If s∈G
p
has order q then there exists an element u∈G
q
such that o(u)=o(s) and
dimuGq=dimsGp\dim u^{G_{q}}=\dim s^{G_{p}}
. 相似文献
17.
Jin-Xing Cai 《manuscripta mathematica》1998,95(1):273-287
LetX, Y be smooth complex projective varieties, andf: X →Y be a fiber space whose general fiber is a curve of genusg. Denote byq
f
the relative irregularity off. It is proved thatq
f
≤5g+1 / 6, iff is not generically trivial; moreover, if either a)f is non-constant and the general fiber is either hyperelliptic or bielliptic or b)q(Y)=0, thenq
f
≤g+1 / 2, and the bound is best possible.
A classification of fiber surfaces of genus 3 withq
f
=2 is also given in this note.
Project supported by China Postdoctoral Science Foundation 相似文献
18.
Gian Pietro Pirola 《manuscripta mathematica》2002,108(2):163-170
In this paper it is proved that a complete algebraic surface of general type with p
g
=q=3, without irrational pencil of genus bigger than one is birationally equivalent to the two-symmetric product of a curve
of genus 3. This result completes the classification of the surfaces with p
g
=q=3. The main tools are the Lefschetz theorem and the use of the paracanonical system on the surface.
Received 14 August 2001 / Revised version: 17 January 2002 相似文献
19.
N. K. Bakirov 《Journal of Mathematical Sciences》1996,81(1):2357-2362
Letξ
i
(t),i=1,2,t ∈ [0, 1], be Gaussian zero mean processes with continous sample paths. Bounds for the probabilitiesβ
i
=P{ξ
i
-α
i
∈B},i=1,2, are given, where aiε C0, 1., and B is a Borel subset of C[0, 1] Bibliography: 5 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 207, pp. 5–12, 1993.
Translated by V. Sudakov. 相似文献
20.
David M. Bressoud 《Proceedings Mathematical Sciences》1987,97(1-3):61-66
Given a basic hypergeometric series with numerator parametersa
1,a
2, ...,a
r and denominator parametersb
2, ...,b
r, we say it isalmost poised ifb
i, =a
1
q
δ,i
a
i,δi = 0, 1 or 2, for 2 ≤i ≤r. Identities are given for almost poised series withr = 3 andr = 5 when a1, =q
−2n.
Partially supported by N.S.F. Grant No. DMS-8521580. 相似文献