共查询到20条相似文献,搜索用时 218 毫秒
1.
CAI Yongmao & SHEN Yuliang Department of Mathematics Suzhou University Suzhou China 《中国科学A辑(英文版)》2006,(5)
It is proved that for any Fuchsian group Г such that H/Г is a hyperbolic Riemann surface, the Teichmuller curve V(Г) has a unique complex manifold structure so that the natural projection of the Bers fiber space F(Г) onto V(Г) is holomorphic with local holomorphic sections. An isomorphism theorem for Teichmuller curves is deduced, which generalizes a classical result that the Teichmuller curve V(Г) depends only on the type of Г and not on the orders of the elliptic elements of Г when H/Г is a compact hyperbolic Riemann surface. 相似文献
2.
In the moduli space M \mathcal{M}
g
of genus-g Riemann surfaces, consider the locus RMO \mathcal{R}{\mathcal{M}_{\mathcal{O}}} of Riemann surfaces whose Jacobians have real multiplication by the order O \mathcal{O} in a totally real number field F of degree g. If g = 3, we compute the closure of RMO \mathcal{R}{\mathcal{M}_{\mathcal{O}}} in the Deligne–Mumford compactification of M \mathcal{M}
g
and the closure of the locus of eigenforms over RMO \mathcal{R}{\mathcal{M}_{\mathcal{O}}} in the Deligne–Mumford compactification of the moduli space of holomorphic 1-forms. For higher genera, we give strong necessary
conditions for a stable curve to be in the boundary of RMO \mathcal{R}{\mathcal{M}_{\mathcal{O}}} . Boundary strata of RMO \mathcal{R}{\mathcal{M}_{\mathcal{O}}} are parameterized by configurations of elements of the field F satisfying a strong geometry of numbers type restriction. 相似文献
3.
4.
This paper focuses on Teichmüller curves in the space of two-genus double covers of flat tori,identifying all of them, counting them with respect to their triangular areas, formulating the numbers of their cusps, and characterizing the ones without a simple cusp. Some applications are also discussed. 相似文献
5.
《Finite Fields and Their Applications》2007,13(1):136-157
Constructing new codes from existing ones by puncturing is in this paper viewed in the context of order domains R where puncturing can be seen as redefinition of the evaluation map . The order domains considered here are of the form where redefining can be done by adding one or more polynomials to the basis of the defining ideal I to form a new ideal J in such a way that the number of points in the variety is reduced by t to form and puncturing in t coordinates is achieved. An explicit construction of such polynomials is given in the case of codes defined by Norm–Trace curves and examples are given of both evaluation codes and dual codes. Finally, it is demonstrated that the improvement in minimum distance can be significant when compared to the lower bound obtained by ordinary puncturing. 相似文献
6.
We prove that the Teichmüller disc stabilized by the Arnoux-Yoccoz pseudo-Anosov diffeomorphism contains at least two closed
Teichmüller geodesics. This proves that the corresponding flat surface does not have a cyclic Veech group.
In addition, we prove that this Teichmüller disc is dense inside the hyperelliptic locus of the connected component (2,2) . The proof uses Ratner’s theorems.
Rephrasing our results in terms of quadratic differentials, we show that there exists a holomorphic quadratic differential,
on a genus 2 surface, with the two following properties:
Received: June 2007, Revision: April 2008, Accepted: April 2008 相似文献
1. | The Teichmüller disc is dense inside the moduli space of holomorphic quadratic differentials (which are not the global square of any Abelian differentials). |
2. | The stabilizer of the ()-action contains two non-commuting pseudo-Anosov diffeomorphisms. |
7.
W. A. Veech 《Inventiones Mathematicae》1989,97(3):553-583
Summary There exists a Teichmüller disc
n
containing the Riemann surface ofy
2+x
n
=1, in the genus [n–1/2] Teichmüller space, such that the stabilizer of
n
in the mapping class group has a fundamental domain of finite (Poincaré) volume in
n
. Application is given to an asymptotic formula for the length spectrum of the billiard in isosceles triangles with angles (/n, /n,n–2/n) and to the uniform distribution of infinite billiard trajectories in the same triangles.
Research supported by NSF-DMS-8521620 相似文献
Research supported by NSF-DMS-8521620 相似文献
8.
We define a divisor theory for graphs and tropical curves endowed with a weight function on the vertices; we prove that the Riemann–Roch theorem holds in both cases. We extend Baker’s Specialization Lemma to weighted graphs. 相似文献
9.
For the Artin–Schreier curve y q ? y = f(x) defined over a finite field \({{\mathbb F}_q}\) of q elements, the celebrated Weil bound for the number of \({{\mathbb F}_{q^r}}\)-rational points can be sharp, especially in super-singular cases and when r is divisible. In this paper, we show how the Weil bound can be significantly improved, using ideas from moment L-functions and Katz’s work on ?-adic monodromy calculations. Roughly speaking, we show that in favorable cases (which happens quite often), one can remove an extra \({\sqrt{q}}\) factor in the error term. 相似文献
10.
11.
First, we give some characterization of hyperbolic embeddedness in the almost complex case. Next, we study the stability of
hyperbolically embedded manifolds under a small perturbation of almost complex structures. Finally, we obtain generalizations
and extensions of theorems of Kobayashi, Kiernan, Kwack and Noguchi for almost complex manifolds. 相似文献
12.
13.
We prove an equivariant Riemann–Roch formula for divisors on algebraic curves over perfect fields. By reduction to the known
case of curves over algebraically closed fields, we first show a preliminary formula with coefficients in . We then prove and shed some further light on a divisibility result that yields a formula with integral coefficients. Moreover,
we give variants of the main theorem for equivariant locally free sheaves of higher rank. 相似文献
14.
15.
In this paper we study 16 complete intersection K3-fibered Calabi--Yau variety types in biprojective space ℙ
n
1}×ℙ1. These are all the CICY-types that are K3 fibered by the projection on the second factor. We prove existence of isolated rational curves of bidegree (d,0) for every positive integer d on a general Calabi–Yau variety of these types. The proof depends heavily on existence theorems for curves on K3-surfaces proved by S. Mori and K. Oguiso. Some of these varieties are related to Calabi–Yau varieties in projective space
by a determinantal contraction, and we use this to prove existence of rational curves of every degree for a general Calabi–Yau
variety in projective space.
Received: 14 October 1997 / Revised version: 18 January 1998 相似文献
16.
Hideki Miyachi 《Geometriae Dedicata》2013,162(1):283-304
In this paper, we study the asymptotic behavior of Teichmüller geodesic rays in the Gardiner–Masur compactification. We will observe that any Teichmüller geodesic ray converges in the Gardiner–Masur compactification. Therefore, we get a mapping from the space of projective measured foliations to the Gardiner–Masur boundary by assigning the limits of associated Teichmüller rays. We will show that this mapping is injective but is neither surjective nor continuous. We also discuss the set of points where this mapping is bicontinuous. 相似文献
17.
An orientation reversing involution of a topological compact genus surface induces an antiholomorphic involution of the Teichmüller space of genus g Riemann surfaces. Two such involutions and are conjugate in the mapping class group if and only if the corresponding orientation reversing involutions and of are conjugate in the automorphism group of . This is equivalent to saying that the quotient surfaces and are homeomorphic. Hence the Teichmüller space has distinct antiholomorphic involutions, which are also called real structures of ([7]). This result is a simple fact that follows from Royden's theorem ([4]) stating that the the mapping class group is
the full group of holomorphic automorphisms of the Teichmüller space (). Let and be two real structures that are not conjugate in the mapping class group. In this paper we construct a real analytic diffeomorphism
such that
This mapping d is a product of full and half Dehn–twists around certain simple closed curves on the surface . This has applications to the moduli spaces of real algebraic curves. A compact Riemann surface admitting an antiholomorphic involution is a real algebraic curve of the topological type . All fixed–points of the real structure of the Teichmüller space , are real curves of the above topological type and every real curve of that topological type is represented by an element
of the fixed–point set of . The fixed–point set is the Teichmüller space of real algebraic curves of the corresponding topological type. Given two different real structures
and , let d the the real analytic mapping satisfying (1). It follows that d maps onto and is an explicit real analytic diffeomorphism between these Teichmüller spaces.
Received 8 December 1997; accepted 12 August 1998 相似文献
18.
We consider a motion of non-closed planar curves with infinite length. The motion is governed by a steepest descent flow for the geometric functional which consists of the sum of the length functional and the total squared curvature. We call the flow shortening–straightening flow. In this paper, first we prove a long time existence result for the shortening–straightening flow for non-closed planar curves with infinite length. Then we show that the solution converges to a stationary solution as time goes to infinity. Moreover we give a classification of the stationary solution. 相似文献
19.
The Hasse–Weil–Serre bound is improved for low genus curves over finite fields with discriminant from by studying maximal and minimal curves. 相似文献
20.
Atsushi Noma 《Journal of Algebra》2009,321(9):2445-2460