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1.
Edoardo Ballico 《Results in Mathematics》2007,50(3-4):169-172
Fix non-negative integers r, e, m, g, s such that r ≥ 3, 0 ≤ m < r, e > 0, g + s ≤ er + max{0, m − 1} + 2, g ≤ (e − 1)r + max{0,m − 1} and 0 ≤ s ≤ er + 2. Set d := er + m. Fix any such that and S is in linearly general position. Fix an ordering of the points P
1, . . . , P
s
of S. Here we prove the existence of an irreducible family Γ of smooth, non-degenerate and connected curves with degree d and genus g, all of them containing S and such that the induced map is dominant.
Received: September 19, 2006. 相似文献
2.
For a (smooth irreducible) curveC of genus g and Clifford indexc>2 with a linear seriesg
d
r
computing c (so
) it is well known thatc + 2 ≤d ≤2 (c + 2), and if
then 2c + 1 ≤g ≤ 2c + 4 unlessd = 2c + 4 in which caseg = 2c + 5.
Let c ≥ 0 andg be integers. If 2c + 1 ≤g ≤2c + 4 we prove that for any integerd <g such thatd ≡c mod 2 andc + 2 ≤d < 2(c + 2) there exists a curve of genus g and Clifford index c with a gd
r computing c. Ford ≥c + 6 (i.e.r ≥ 3) we construct this curve on a surface of degree 2r-2 in ℙr, and ford ≥c + 8 (i.e.r ≥ 4) we show that such a curve cannot be found on a surface in ℙr of smaller degree. In fact, if gd
r computes the Clifford index c of C such thatc + 8 ≤d ≤ 2c + 3 then the birational morphism defined by this series cannot map C onto a (maybe, singular) curve contained in a surface
of degree at most 2r-3 in ℙr. 相似文献
3.
The (d, m)-domination number γd,m is a new measure to characterize the reliability of resources-sharing in fault tolerant networks, in some sense, which can more accurately characterize the reliability of networks than the m-diameter does. In this paper, we study the (d, 4)-domination numbers of undirected toroidal mesh Cd1 × Cd2 for some special values of d, obtain that γd,4 (Cd1 × C3) = 2 if and only if d4(G) e1 ≤ d d4(G) for d1 ≥ 5, γd,4 (Cd1 × C4) = 2 if d4(G) (2e1-[d1+e1]/2) ≤ d d4(G) for d1 ≥ 24, and γd,4 (Cd1 × Cd2 ) = 2 if d4(G) ( e1-2) ≤ d d4(G) for d1 = d2 ≥ 14. 相似文献
4.
Francesca Vetro 《manuscripta mathematica》2008,125(3):353-368
Let Y be a smooth, connected, projective complex curve. In this paper, we study the Hurwitz spaces which parameterize branched
coverings of Y whose monodromy group is a Weyl group of type D
d
and whose local monodromies are all reflections except one. We prove the irreducibility of these spaces when and successively we extend the result to curves of genus g ≥ 1. 相似文献
5.
E. Ballico 《Annali dell'Universita di Ferrara》1999,45(1):123-125
Fix integersg, k andt witht>0,k≥3 andtk<g/2−1. LetX be a generalk-gonal curve of genusg andR∈Pic
k
(X) the uniqueg
k
1
onX. SetL:=K
X⊗(R
*)⊗t.L is very ample. Leth
L:X→P(H
0(X, L)*) be the associated embedding. Here we prove thath
L(X) is projectively normal. Ifk≥4 andtk<g/2−2 the curveh
L(X) is scheme-theoretically cut out by quadrics.
The author was partially supported by MURST and GNSAGA of CNR (Italy). 相似文献
6.
We consider the g-ary expansion N=∑ k b k (N, g)g k of non-negative integers N and prove various results on the distribution and the mean value of the k-th digit b k (N, g) if g varies in an interval of the form 2≤g≤N η. As an application we also consider the average value of the sum-of-digits function s(N, g)=∑ k b k (N, g). 相似文献
7.
Robin Hartshorne 《Annali dell'Universita di Ferrara》1994,40(1):207-223
LetC be a curve contained in ℙ
k
3
(k of any characteristic), which is locally Cohen-Macaulay, not contained in a plane and of degreed. We prove thatp
a
(C)≤≤((d−2)(d−3))/2. Moreover we show existence of curves with anyd, p
a
satisfying this inequality and we characterize those curves for which equality holds.
Sunto Si dimostra che seC⊃ℙ k 3 (k di caratteristica qualunque) é una curva, non piana, localmente Cohen-Macaulay, di gradod, allorap a (C)≤((d−2)(d−3))/2. Si mostra che questa limitazione è ottimale, e si classificano le curve di genere aritmetico massimale.相似文献
8.
We consider the g-ary expansion N=∑
k
b
k
(N, g)g
k
of non-negative integers N and prove various results on the distribution and the mean value of the k-th digit b
k
(N, g) if g varies in an interval of the form 2≤g≤N
η. As an application we also consider the average value of the sum-of-digits function s(N, g)=∑
k
b
k
(N, g).
Received 5 November 2001
RID="a"
ID="a" Dedicated to Professor Edmund Hlawka on the occasion of his 85th birthday 相似文献
9.
Marc Coppens Gerriet Martens 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》1999,69(1):347-371
This paper is a contribution towards a Brill-Noether theory for the moduli space of smooth &-gonal curves of genusg. Specifically, we prove the existence of certain special divisors on a generalk-gonal curveC of genusg, and we detect an irreducible component of the “expected” dimension in the varietyW
r
d
(C), (r ≤k — 2) of special divisors ofC. The latter induces a new proof of the existence theorem for special divisors on a smooth curve. 相似文献
10.
We consider Dirichlet series zg,a(s)=?n=1¥ g(na) e-ln s{\zeta_{g,\alpha}(s)=\sum_{n=1}^\infty g(n\alpha) e^{-\lambda_n s}} for fixed irrational α and periodic functions g. We demonstrate that for Diophantine α and smooth g, the line Re(s) = 0 is a natural boundary in the Taylor series case λ
n
= n, so that the unit circle is the maximal domain of holomorphy for the almost periodic Taylor series ?n=1¥ g(na) zn{\sum_{n=1}^{\infty} g(n\alpha) z^n}. We prove that a Dirichlet series zg,a(s) = ?n=1¥ g(n a)/ns{\zeta_{g,\alpha}(s) = \sum_{n=1}^{\infty} g(n \alpha)/n^s} has an abscissa of convergence σ
0 = 0 if g is odd and real analytic and α is Diophantine. We show that if g is odd and has bounded variation and α is of bounded Diophantine type r, the abscissa of convergence σ
0 satisfies σ
0 ≤ 1 − 1/r. Using a polylogarithm expansion, we prove that if g is odd and real analytic and α is Diophantine, then the Dirichlet series ζ
g,α
(s) has an analytic continuation to the entire complex plane. 相似文献
11.
Let Ω ⊂ ℝ
N
be a smooth bounded domain such that 0 ∈ Ω,N≥3, 0≤s<2,2* (s)=2(N−s)/(N−2). We prove the existence of nontrival solutions for the singular critical problem
with Dirichlet boundary condition on Ω for suitable positive parameters λ and μ.
Corresponding author. This work is supported partly by the National Natural Science Foundation of China (No. 10171036) and
the Natural Science Foundation of South-Central University For Nationalities (No. YZZ03001). The authors sincerely thank Prof.
Daomin Cao (AMSS, Chinese Academy of Sciences) for helpful discussions and suggestions. 相似文献
12.
Let C be an algebraic curve of genus g ≥ 2. We prove an analogue of Clifford’s theorem for coherent systems on C and some refinements using results of Re and Mercat.
Received: 27 July 2007 相似文献
13.
Hartmut Bauer 《Mathematische Zeitschrift》2006,254(2):219-237
We generalize a result of Max Deuring on the zeros of Zeta-function of quadratic forms to Asai's non-holomophic Eisenstein
series E(z,s) of the Hilbert modular group. We prove that inside the rectangular
and −1≤Re(s) ≤ 2 the function E(z,s) has only simple zeros on the line Re(s)=1/2 and two simple real zeros, if |N(y)| is large.
The research was supported by a fellowship within the Post-doc-Program of the DAAD (German Academic Exchange Service) 相似文献
14.
We consider the Cauchy problem for a second order weakly hyperbolic equation, with coefficients depending only on the time
variable. We prove that if the coefficients of the equation belong to the Gevrey class gs0\gamma^{s_{0}} and the Cauchy data belong to gs1\gamma^{s_{1}}, then the Cauchy problem has a solution in
gs0([0,T*];gs1(\mathbbR))\gamma^{s_{0}}([0,T^{*}];\gamma^{s_{1}}(\mathbb{R})) for some T
*>0, provided 1≤s
1≤2−1/s
0. If the equation is strictly hyperbolic, we may replace the previous condition by 1≤s
1≤s
0. 相似文献
15.
Gil Kalai 《Discrete and Computational Geometry》1988,3(1):1-14
Lets(d, n) be the number of triangulations withn labeled vertices ofS
d–1, the (d–1)-dimensional sphere. We extend a construction of Billera and Lee to obtain a large family of triangulated spheres. Our construction shows that logs(d, n)C
1(d)n
[(d–1)/2], while the known upper bound is logs(d, n)C
2(d)n
[d/2] logn.Letc(d, n) be the number of combinatorial types of simpliciald-polytopes withn labeled vertices. (Clearly,c(d, n)s(d, n).) Goodman and Pollack have recently proved the upper bound: logc(d, n)d(d+1)n logn. Combining this upper bound forc(d, n) with our lower bounds fors(d, n), we obtain, for everyd5, that lim
n(c(d, n)/s(d, n))=0. The cased=4 is left open. (Steinitz's fundamental theorem asserts thats(3,n)=c(3,n), for everyn.) We also prove that, for everyb4, lim
d(c(d, d+b)/s(d, d+b))=0. (Mani proved thats(d, d+3)=c(d, d+3), for everyd.)Lets(n) be the number of triangulated spheres withn labeled vertices. We prove that logs(n)=20.69424n(1+o(1)). The same asymptotic formula describes the number of triangulated manifolds withn labeled vertices.Research done, in part, while the author visited the mathematics research center at AT&T Bell Laboratories. 相似文献
16.
We study in detail locally Cohen-Macaulay curves in P4 which are contained in a double plane 2H, thus completing the classification of curves lying on surfaces of degree two. We describe the irreducible components of the Hilbert schemes H d,g(2H) of lo-cally Cohen-Macaulay curves in 2H of degree d and arithmetic genus g, and we show that H d,g(2H) is connected. We also discuss the Rao module of these curves and liaison and biliaison equiva-lence classes. 相似文献
17.
QU Yanhui WEN Shengyou & WEN Zhiying Department of Mathematics Tsinghua University Beijing China Department of Mathematics Hubei University Wuhan China 《中国科学A辑(英文版)》2005,48(11):1545-1553
In this paper, the relationship between the s-dimensional Hausdorff measures and the g-measures in Rd is discussed, where g is a gauge function which is equivalent to ts and 0 < s≤d. It shows that if s=d, then Hg = c1Hd, Cg = c2Cd and Pg = c3Pd on Rd, where constants c1, c2 and c3 are determined by where Wg, Cg and Pg are the g-Hausdorff, g-central Hausdorff and g-packing measures on Rd respectively. In the case 0相似文献
18.
We call an element of a finite general linear group GL(d, q) fat if it leaves invariant and acts irreducibly on a subspace of dimension greater than d/2. Fatness of an element can be decided efficiently in practice by testing whether its characteristic polynomial has an irreducible
factor of degree greater than d/2. We show that for groups G with SL(d, q) ≤ G ≤ GL(d, q) most pairs of fat elements from G generate irreducible subgroups, namely we prove that the proportion of pairs of fat elements generating a reducible subgroup,
in the set of all pairs in G × G, is less than q
−d+1. We also prove that the conditional probability to obtain a pair (g
1, g
2) in G × G which generates a reducible subgroup, given that g
1, g
2 are fat elements, is less than 2q
−d+1. Further, we show that any reducible subgroup generated by a pair of fat elements acts irreducibly on a subspace of dimension
greater than d/2, and in the induced action the generating pair corresponds to a pair of fat elements. 相似文献
19.
We will study the following problem.Let X_t,t∈[0,T],be an R~d-valued process defined on atime interval t∈[0,T].Let Y be a random value depending on the trajectory of X.Assume that,at each fixedtime t≤T,the information available to an agent(an individual,a firm,or even a market)is the trajectory ofX before t.Thus at time T,the random value of Y(ω) will become known to this agent.The question is:howwill this agent evaluate Y at the time t?We will introduce an evaluation operator ε_t[Y] to define the value of Y given by this agent at time t.Thisoperator ε_t[·] assigns an (X_s)0(?)s(?)T-dependent random variable Y to an (X_s)0(?)s(?)t-dependent random variableε_t[Y].We will mainly treat the situation in which the process X is a solution of a SDE (see equation (3.1)) withthe drift coefficient b and diffusion coefficient σcontaining an unknown parameter θ=θ_t.We then consider theso called super evaluation when the agent is a seller of the asset Y.We will prove that such super evaluation is afiltration consistent nonlinear expectation.In some typical situations,we will prove that a filtration consistentnonlinear evaluation dominated by this super evaluation is a g-evaluation.We also consider the correspondingnonlinear Markovian situation. 相似文献
20.
Deguang Han 《Journal of Fourier Analysis and Applications》2009,15(2):201-217
Let
be a full rank time-frequency lattice in ℝ
d
×ℝ
d
. In this note we first prove that any dual Gabor frame pair for a Λ-shift invariant subspace M can be dilated to a dual Gabor frame pair for the whole space L
2(ℝ
d
) when the volume v(Λ) of the lattice Λ satisfies the condition v(Λ)≤1, and to a dual Gabor Riesz basis pair for a Λ-shift
invariant subspace containing M when v(Λ)>1. This generalizes the dilation result in Gabardo and Han (J. Fourier Anal. Appl. 7:419–433, [2001]) to both higher dimensions and dual subspace Gabor frame pairs. Secondly, for any fixed positive integer N, we investigate the problem whether any Bessel–Gabor family G(g,Λ) can be completed to a tight Gabor (multi-)frame G(g,Λ)∪(∪
j=1
N
G(g
j
,Λ)) for L
2(ℝ
d
). We show that this is true whenever v(Λ)≤N. In particular, when v(Λ)≤1, any Bessel–Gabor system is a subset of a tight Gabor frame G(g,Λ)∪G(h,Λ) for L
2(ℝ
d
). Related results for affine systems are also discussed.
Communicated by Chris Heil. 相似文献