共查询到20条相似文献,搜索用时 31 毫秒
1.
Elena Mantovan 《Mathematische Annalen》2008,340(2):265-292
We investigate the notion of Igusa level structure for a one-dimensional Barsotti–Tate group over a scheme X of positive characteristic and compare it to Drinfeld’s notion of level structure. In particular, we show how the geometry
of the Igusa covers of X is useful for studying the geometry of its Drinfeld covers (e.g. connected and smooth components, singularities). Our results
apply in particular to the study of the Shimura varieties considered in Harris and Taylor (On the geometry and cohomology
of some simple Shimura varieties. Princeton University Press, Princeton, 2001). In this context, they are higher dimensional
analogues of the classical work of Igusa for modular curves and of the work of Carayol for Shimura curves. In the case when
the Barsotti–Tate group has constant p-rank, this approach was carried-out by Harris and Taylor (On the geometry and cohomology of some simple Shimura varieties.
Princeton University Press, Princeton, 2001). 相似文献
2.
We consider linear error correcting codes associated to higher-dimensional projective varieties defined over a finite field. The problem of determining the basic parameters of such codes often leads to some interesting and difficult questions in combinatorics and algebraic geometry. This is illustrated by codes associated to Schubert varieties in Grassmannians, called Schubert codes, which have recently been studied. The basic parameters such as the length, dimension and minimum distance of these codes are known only in special cases. An upper bound for the minimum distance is known and it is conjectured that this bound is achieved. We give explicit formulae for the length and dimension of arbitrary Schubert codes and prove the minimum distance conjecture in the affirmative for codes associated to Schubert divisors. 相似文献
3.
Carolina Araujo 《Mathematische Zeitschrift》2010,264(1):179-193
In these notes, we investigate the cone of nef curves of projective varieties, which is the dual cone to the cone of pseudo-effective
divisors. We prove a structure theorem for the cone of nef curves of projective
\mathbb Q{\mathbb Q}-factorial klt pairs of arbitrary dimension from the point of view of the Minimal Model Program. This is a generalization
of Batyrev’s structure theorem for the cone of nef curves of projective terminal threefolds. 相似文献
4.
Anna Dall’Acqua 《Annals of Global Analysis and Geometry》2012,42(3):411-420
We give a sufficient condition for curves on a plane or on a sphere such that if these give the boundary of a Willmore surface touching tangentially along the boundary the plane or the sphere respectively, the surface is necessarily a piece of the plane or a piece of the sphere. The condition we require is that the curves bound a strictly star-shaped domain with respect to the Euclidean geometry in the plane and with respect to the spherical geometry in the sphere, respectively. 相似文献
5.
A. G. Aleksandrov 《Functional Analysis and Its Applications》2017,51(4):245-254
In the article we introduce the notion of logarithmic differential forms with poles along a Cartier divisor given on a variety with singularities, discuss some properties of such forms, and describe highly efficient methods for computing the Poincaré series and generators of modules of logarithmic differential forms in various situations. We also examine several concrete examples by applying these methods to the study of divisors on varieties with singularities of many types, including quasi-homogeneous complete intersections, normal, determinantal, and rigid varieties, and so on. 相似文献
6.
Antony Maciocia 《Mathematische Nachrichten》2012,285(16):1981-1998
We study twisted ideal sheaves of small length on an irreducible principally polarized abelian surface $({\mathbb T},\ell )We study twisted ideal sheaves of small length on an irreducible principally polarized abelian surface $({\mathbb T},\ell )$. Using Fourier‐Mukai techniques we associate certain jumping schemes to such sheaves and completely classify such loci. We give examples of applications to the enumerative geometry of ${\mathbb T}$ and show that no smooth genus 5 curve on such a surface can contain a $g^1_3$. We also describe explicitly the singular divisors in the linear system |2?|. 相似文献
7.
A. Rittatore 《Transformation Groups》1998,3(4):375-396
We study the geometry of algebraic monoids. We prove that the group of invertible elements of an irreducible algebraic monoid
is an algebraic group, open in the monoid. Moreover, if this group is reductive, then the monoid is affine. We then give a
combinatorial classification of reductive monoids by means of the theory of spherical varieties.
Partially supported by a CONICYT's grant and the Universidad de la República (Uruguay) 相似文献
8.
We prove that every topological conjugacy between two germs of singular holomorphic curves in the complex plane is homotopic to another conjugacy which extends homeomorphically to the exceptional divisors of their minimal desingularisations. As an application we give an explicit presentation of a finite index subgroup of the mapping class group of the germ of such a singularity. 相似文献
9.
These notes are an introduction to wonderful varieties. We discuss some general results on their geometry, their role in the theory of spherical varieties, several aspects of the combinatorics arising from these varieties, and some examples. 相似文献
10.
Francisco Luis Rocha Pimentel 《Geometriae Dedicata》2001,85(1-3):125-134
We present a new result on the geometry of nonhyperelliptic curves; namely, the intersection divisors of a canonically embedded curve C with its osculating spaces at a point P, not considering the intersection at P, can only vary in dimensions given by the Weierstrass semigroup of the curve C at P. We obtain, under a reasonable geometrical hypothesis, monomial bases for the spaces of higher-order regular differentials. We also give a sufficient condition on the Weierstrass semigroup of C at P in order for this geometrical hypothesis to be true. Finally, we give examples of Weierstrass semigroups satisfying this condition. 相似文献
11.
Carolina Araujo 《Geometriae Dedicata》2009,139(1):289-297
In this paper we characterize smooth complex projective varieties that admit a quadric bundle structure on some dense open
subset in terms of the geometry of certain families of rational curves.
相似文献
12.
In Duursma and Park (2010) [7], the authors formulate new coset bounds for algebraic geometric codes. The bounds give improved lower bounds for the minimum distance of algebraic geometric codes as well as improved thresholds for algebraic geometric linear secret sharing schemes. The bounds depend on the delta set of a coset and on the choice of a sequence of divisors inside the delta set. In this paper we give general properties of delta sets and we analyze sequences of divisors supported in two points on Hermitian and Suzuki curves. 相似文献
13.
The article is devoted to the study of the classification problem for Saito free divisors making use of the deformation theory of varieties. In particular, in the quasihomogeneous case, we describe an approach for computation of free deformations of quasicones over quasismooth varieties based on properties of deformations of varieties with $ {\mathbb{G}_m} $ -action. We also discuss some applications including the problem of compactification of modular spaces and computation of free deformations for certain simple, unimodal, and unimodular singularities. 相似文献
14.
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
15.
Min Ru 《数学学报(英文版)》2018,34(8):1208-1224
In 2002, in the paper entitled “A subspace theorem approach to integral points on curves”, Corvaja and Zannier started the program of studying integral points on algebraic varieties by using Schmidt’s subspace theorem in Diophantine approximation. Since then, the program has led a great progress in the study of Diophantine approximation. It is known that the counterpart of Schmidt’s subspace in Nevanlinna theory is H. Cartan’s Second Main Theorem. In recent years, the method of Corvaja and Zannier has been adapted by a number of authors and a big progress has been made in extending the Second Main Theorem to holomorphic mappings from C into arbitrary projective variety intersecting general divisors by using H. Cartan’s original theorem. We call such method “a Cartan’s Second Main Theorem approach”. In this survey paper, we give a systematic study of such approach, as well as survey some recent important results in this direction including the recent work of the author with Paul Voja. 相似文献
16.
Publications mathématiques de l'IHÉS - In this paper, we investigate the geometry of projective varieties polarised by ample and more generally nef and big Weil divisors. First we... 相似文献
17.
Enrique Artal Bartolo Shinzo Bannai Taketo Shirane Hiro-o Tokunaga 《Mathematische Nachrichten》2023,296(6):2214-2235
There is a close relationship between the embedded topology of complex plane curves and the (group-theoretic) arithmetic of elliptic curves. In a recent paper, we studied the topology of some arrangements of curves that include a special smooth component, via the torsion properties induced by the divisors in the special curve associated to the remaining components, which is an arithmetic property. When this special curve has maximal flexes, there is a natural isomorphism between its Jacobian variety and the degree zero part of its Picard group. In this paper, we consider curve arrangements that contain a special smooth component with a maximal flex and exploit these properties to obtain Zariski tuples, which show the interplay between topology, geometry, and arithmetic. 相似文献
18.
Shuichi Iida 《Mathematische Annalen》2010,346(3):669-717
We construct a function on the orbifold fundamental group of the moduli space of smooth theta divisors, which we call the
Meyer function for smooth theta divisors. In the construction, we use the adiabatic limits of the η-invariants of the mapping torus of theta divisors. We shall prove that the Meyer function for smooth theta divisors cobounds
the signature cocycle, and we determine the values of the Meyer function for the Dehn twists. In particular, we give an analytic
construction of the Meyer function of genus two. 相似文献
19.
Takuro Abe 《Transactions of the American Mathematical Society》2007,359(9):4285-4295
We give a generalized definition of an elementary transformation of vector bundles on regular schemes by using Maximal Cohen-Macaulay sheaves on divisors. This definition is a natural extension of that given by Maruyama, and has a connection with that given by Sumihiro. By this elementary transformation, we can construct, up to tensoring line bundles, all vector bundles from trivial bundles on nonsingular quasi-projective varieties over an algebraically closed field. Moreover, we give an application of this theory to reflexive sheaves.
20.
Olivier Penacchio 《Mathematische Nachrichten》2011,284(4):526-542
We describe an equivalence of categories between the category of mixed Hodge structures and a category of equivariant vector bundles on a toric model of the complex projective plane which verify some semistability condition. We then apply this correspondence to define an invariant which generalizes the notion of R ‐split mixed Hodge structure and give calculations for the first group of cohomology of possibly non smooth or non‐complete curves of genus 0 and 1. Finally, we describe some extension groups of mixed Hodge structures in terms of equivariant extensions of coherent sheaves. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim 相似文献