共查询到20条相似文献,搜索用时 15 毫秒
1.
Let S be a smooth projective surface. Here we study the conditions imposed to curves of a fixed very ample linear system by a general
union of types of singularities τ when most of connected components of τ are ordinary double points. This problem is related
to the existence of “good” families of curves on S with prescribed singularities, most of them being nodes, and to the regularity of their Hilbert scheme.
Received 6 July 2000; in revised form 16 June 2001 相似文献
2.
Let S be a closed Riemann surface of genus g. It is well known that there are Schottky groups producing uniformizations of S (Retrosection Theorem). Moreover, if τ: S → S is a conformal involution, it is also known that there is a Kleinian group K containing, as an index two subgroup, a Schottky group G that uniformizes S and so that K/G induces the cyclic group 〈τ〉. Let us now assume S is a stable Riemann surface and τ: S → S is a conformal involution. Again, it is known that S can be uniformized by a suitable noded Schottky group, but it is not known whether or not there is a Kleinian group K, containing a noded Schottky group G of index two, so that G uniformizes S and K/G induces 〈τ〉. In this paper we discuss this existence problem and provide some partial answers: (1) a complete positive answer for genus
g ≤ 2 and for the case that S/〈τ〉 is of genus zero; (2) the existence of a Kleinian group K uniformizing the quotient stable Riemann orbifold S/〈τ〉. Applications to handlebodies with orientation-preserving involutions are also provided. 相似文献
3.
Let M be a type I von Neumann algebra with the center Z, and a faithful normal semi-finite trace τ. Consider the algebra L(M, τ) of all τ-measurable operators with respect to M and let S
0(M, τ) be the subalgebra of τ-compact operators in L(M, τ). We prove that any Z-linear derivation of S
0(M, τ) is spatial and generated by an element from L(M, τ).
相似文献
4.
Marilyn Breen 《Archiv der Mathematik》1997,68(1):60-64
Let S be a nonempty closed, simply connected set in the plane, and let α τ; 0. If every three points of 5 see a common point of
S via paths of length at most α, then for some point s0 of S, s0 sees each point of S via such a path. That is, S is starshaped via paths of length at most α.
Supported in part by NSF grant DMS-9207019 相似文献
5.
A spherical τ -design on S
n-1
is a finite set such that, for all polynomials f of degree at most τ , the average of f over the set is equal to the average of f over the sphere S
n-1
. In this paper we obtain some necessary conditions for the existence of designs of odd strengths and cardinalities. This
gives nonexistence results in many cases. Asymptotically, we derive a bound which is better than the corresponding estimation
ensured by the Delsarte—Goethals—Seidel bound. We consider in detail the strengths τ =3 and τ =5 and obtain further nonexistence results in these cases. When the nonexistence argument does not work, we obtain bounds
on the minimum distance of such designs.
Received January 30, 1997, and in revised form November 29, 1997. 相似文献
6.
LetS be a bounded region inR
N and let ℊ={S
i}
i
=1/m
be a partition ofS into a finite number of subsets having piecewiseC
2 boundaries. We assume that whereC
2 segments of the boundaries meet, the angle subtended by tangents to these segments at the point of contact is bounded away
from 0. Letτ:S →S be piecewiseC
2 on ℊ and expanding in the sense that there exists 0<σ< 1 such that for anyi=1, 2, ...,m, ‖Dτ
i
−1
‖<σ, whereDτ
i
−1
is the derivative matrix ofτ
i
−1
and ‖ ‖ is the euclidean matrix norm. The main result provides an upper bound onσ which guarantees the existence of an absolutely continuous invariant measure forτ.
The research of the second author was supported by NSERC and FCAR grants. 相似文献
7.
Summary The formal asymptotic analysis of Latifi et al. [4] suggests that the Mixmaster Universe model possesses movable transcendental
singularities and thus is nonintegrable in the sense that it does not satisfy the Painlevé property (i.e., singularities with
nonalgebraic branching). In this paper, we present numerical evidence of the nonintegrability of the Mixmaster model by studying
the singularity patterns in the complext-plane, wheret is the “physical” time, as well as in the complex τ-plane, where τ is the associated “logarithmic” time. More specifically,
we show that in the τ-plane there appears to exist a “natural boundary” of remarkably intricate structure. This boundary lies
at the ends of a sequence of smaller and smaller “chimneys” and consists of the type of singularities studied in [4], on which
pole-like singularities accumulate densely. We also show numerically that in the complext-plane there appear to exist complicated, dense singularity patterns and infinitely-sheeted solutions with sensitive dependence
on initial conditions. 相似文献
8.
Elliptic curve cryptosystems (ECCs) have become increasingly popular due to their efficiency and the small size of the keys
they use. Particularly, the anomalous curves introduced by Koblitz allow a complex representation of the keys, denoted τNAF, that make the computations over these curves more efficient. In this article, we propose an efficient method for randomizing
a τNAF to produce different equivalent representations of the same key to the same complex base τ. We prove that the average Hamming density of the resulting representations is 0.5. We identify the pattern of the τNAFs yielding the maximum number of representations and the formula governing this number. We also present deterministic methods
to compute the average and the exact number of possible representations of a τNAF.
相似文献
9.
Ali Ghaffari 《Semigroup Forum》2008,76(1):95-106
Let S be a foundation locally compact topological semigroup. Two new topologies τ
c
and τ
w
are introduced on M
a
(S)*. We introduce τ
c
and τ
w
almost periodic functionals in M
a
(S)*. We study these classes and compare them with each other and with the norm almost periodic and weakly almost periodic functionals.
For f∈M
a
(S)*, it is proved that T
f
∈ℬ(M
a
(S),M
a
(S)*) is strong almost periodic if and only if f is τ
c
-almost periodic. Indeed, we have obtained a generalization of a well known result of Crombez for locally compact group to
a more general setting of foundation topological semigroups. Finally if P(S) (the set of all probability measures in M
a
(S)) has the semiright invariant isometry property, it is shown that the set of τ
w
-almost periodic functionals has a topological left invariant mean. 相似文献
10.
Summary We consider flat families of reduced curves on a smooth surfaceS such that each memberC has the same number of singularities and each singularity has a fixed singularity type (up to analytic resp. topological
equivalence). We show that these families are represented by a schemeH and give sufficient conditions for the smoothness ofH (atC). Our results improve previously known criteria for families with fixed analytic singularity type and seem to be quite sharp
for curves in ℙ2 of small degree. Moreover, for families with fixed topological type this paper seems to be the first in which arbitrary singularities
are treated.
This article was processed by the author using the LATEX style filecljour1 from Springer-Verlag. 相似文献
11.
LetX be a Riemann surface of genusg. The surfaceX is called elliptic-hyperelliptic if it admits a conformal involutionh such that the orbit spaceX/〈h〉 has genus one. The involutionh is then called an elliptic-hyperelliptic involution. Ifg>5 then the involutionh is unique, see [A]. We call symmetry to any anticonformal involution ofX. LetAut
±(X) be the group of conformal and anticonformal automorphisms ofX and letσ, τ be two symmetries ofX with fixed points and such that {σ, hσ} and {τ, hτ} are not conjugate inAut
±(X). We describe all the possible topological conjugacy classes of {σ, σh, τ, τh}. As consequence of our study we obtain that, in the moduli space of complex algebraic curves of genusg (g even >5), the subspace whose elements are the elliptic-hyperelliptic real algebraic curves is not connected. This fact contrasts
with the result in [Se]: the subspace whose elements are the hyperelliptic real algebraic curves is connected.
The authors are supported by BFM2002-04801. 相似文献
12.
Domenico Perrone 《Archiv der Mathematik》1997,68(4):347-352
Let CP
n
be the n-dimensional complex projective space with the Study-Fubini metric of constant holomorphic sectional curvature 4 and let M be a compact, orientable, n-dimensional totally real minimal submanifold of CP
n
. In this paper we prove the following results.
Supported by funds of the M.U.R.S.T. 相似文献
(a) | If M is 6-dimensional, conformally flat and has non negative Euler number and constant scalar curvature τ, 0<τ ≦ 70/3, then M is locally isometric to S 1,5 :=S 1 (sin θ cos θ) × S 5 (sin θ), tan θ = √6. |
(b) | If M is 4-dimensional, has parallel second fundamental form and scalar curvature τ ≧ 15/2, then M is locally isometric to S 1,3 :=S 1 (sin θ cos θ) × S 3 (sinθ), tan θ=2, or it is totally geodesic. |
13.
LetT(S) be the Teichmüller space of a Riemann surfaceS. By definition, a geodesic disc inT(S) is the image of an isometric embedding of the Poincaré disc intoT(S). It is shown in this paper that for any non-Strebel pointτ ∈ T(S), there are infinitely many geodesic discs containing [0] and τ. 相似文献
14.
Let (G, K) be a Riemannian symmetric pair of maximal rank, where G is a compact simply connected Lie group and K is the fixed point set of an involutive automorphism σ. This induces an involutive automorphism τ of the based loop space Ω(G). There exists a maximal torus T ⊂ G such that the canonical action of T × S
1 on Ω(G) is compatible with τ (in the sense of Duistermaat). This allows us to formulate and prove a version of Duistermaat’s convexity theorem. Namely,
the images of Ω(G) and Ω(G)
τ
(fixed point set of τ) under the T × S
1 moment map on Ω(G) are equal. The space Ω(G)
τ
is homotopy equivalent to the loop space Ω(G/K) of the Riemannian symmetric space G/K. We prove a stronger form of a result of Bott and Samelson which relates the cohomology rings with coefficients in
\mathbbZ2 {\mathbb{Z}_2} of Ω(G) and Ω(G/K). Namely, the two cohomology rings are isomorphic, by a degree-halving isomorphism (Bott and Samelson [BS] had proved that the Betti numbers are equal). A version of this theorem involving equivariant cohomology is also proved.
The proof uses the notion of conjugation space in the sense of Hausmann, Holm, and Puppe [HHP]. 相似文献
15.
We describe the statistics of repetition times of a string of symbols in a stochastic process.
Denote by τ
A
the time elapsed until the process spells a finite string A and by S
A
the number of consecutive repetitions of A. We prove that, if the length of the string grows unboundedly, (1) the distribution of τ
A
, when the process starts with A, is well approximated by a certain mixture of the point measure at the origin and an exponential law, and (2) S
A
is approximately geometrically distributed. We provide sharp error terms for each of these approximations. The errors we
obtain are point-wise and also allow us to get approximations for all the moments of τ
A
and S
A
. To obtain (1) we assume that the process is φ-mixing, while to obtain (2) we assume the convergence of certain conditional probabilities.
相似文献
16.
Qiu 《Semigroup Forum》2008,66(1):131-139
Abstract. The concept of pseudo-regular S -system is introduced. A torsion theory τ
u
= ( U
S
, \bar U
S
) with its torsion class U
S
consisting of pseudo-regular S -systems, is constructed. Its corresponding quasi-filter is completely described. A number of results on the relations between
τ
u
and two special torsion theories, the stable and Lambek torsion theories, are obtained. 相似文献
17.
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
18.
Richard Haydon 《Israel Journal of Mathematics》1978,31(2):142-152
In a previous paper (Israel J. Math.28 (1977), 313–324), it was shown that for a certain class of cardinals τ,l
1(τ) embeds in a Banach spaceX if and only ifL
1([0, 1]τ) embeds inX
*. An extension (to a rather wider class of cardinals) of the basic lemma of that paper is here applied so as to yield an affirmative
answer to a question posed by Rosenthal concerning dual ℒ1-spaces. It is shown that ifZ
* is a dual Banach space, isomorphic to a complemented subspace of anL
1-space, and κ is the density character ofZ
*, thenl
1(κ) embeds inZ
*. A corollary of this result is that every injective bidual Banach space is isomorphic tol
∞(κ) for some κ. The second part of this article is devoted to an example, constructed using the continuum hypothesis, of a
compact spaceS which carries a homogeneous measure of type ω1, but which is such thatl
1(ω1) does not embed in ℰ(S). This shows that the main theorem of the already mentioned paper is not valid in the case τ = ω1. The dual space ℰ(S)* is isometric to
, and is a member of a new isomorphism class of dualL
1-spaces. 相似文献
19.
N. V. Proskurin 《Journal of Mathematical Sciences》2007,143(3):3137-3148
The paper studies the function L(τ;·) defined by the Dirichlet series
, where τ(υ) is the υth Fourier coefficient of the Kubota-Patterson cubic theta function. For this function, an exact and
an approximate functional equations are derived. It is established that the function does not vanish in the halfplane Re s ≥ 1.3533 and has no singularities except for a simple pole at the point 5/6. Issues related to computing the coefficients
τ(υ) and values of the special functions arising in the approximate functional equation are considered. Bibliography: 11 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 337, 2006, pp. 212–232. 相似文献
20.
Satoshi Murai 《Arkiv f?r Matematik》2007,45(2):327-336
In this paper, the relation between algebraic shifting and join which was conjectured by Eran Nevo will be proved. Let σ and
τ be simplicial complexes and σ*τ be their join. Let J
σ be the exterior face ideal of σ and Δ(σ) the exterior algebraic shifted complex of σ. Assume that σ*τ is a simplicial complex
on [n]={1,2,...,n}. For any d-subset S⊂[n], let denote the number of d-subsets R∈σ which are equal to or smaller than S with respect to the reverse lexicographic order. We will prove that for all S⊂[n]. To prove this fact, we also prove that for all S⊂[n] and for all nonsingular matrices ϕ, where Δϕ(σ) is the simplicial complex defined by . 相似文献