共查询到20条相似文献,搜索用时 46 毫秒
1.
Wenxuan Lu 《中国科学 数学(英文版)》2006,49(1):54-65
Hodge integrals over moduli spaces of curves appear naturally during the localization procedure in computation of Gromov-Witten invariants. A remarkable formula of Marino-Vafa expresses a generation function of Hodge integrals via some combinatorial and algebraic data seemingly unrelated to these apriori algebraic geometric objects. We prove in this paper by directly expanding the formula and estimating the involved terms carefully that except a specific type all the other Hodge integrals involving up to three Hodge classes can be calculated from this formula. This implies that amazingly rich information about moduli spaces and Gromov-Witten invariants is encoded in this complicated formula. We also give some low genus examples which agree with the previous results in literature. Proofs and calculations are elementary as long as one accepts Mumford relations on the reductions of products of Hodge classes. 相似文献
2.
Anatoly Libgober 《manuscripta mathematica》2009,128(1):1-31
We show that closures of families of unitary local systems on quasiprojective varieties for which the dimension of a graded
component of Hodge filtration has a constant value can be identified with a finite union of polytopes. We also present a local
version of this theorem. This yields the “Hodge decomposition” of the set of unitary local systems with a non-vanishing cohomology
extending Hodge decomposition of characteristic varieties of links of plane curves studied by the author earlier. We consider
a twisted version of the characteristic varieties generalizing the twisted Alexander polynomials. Several explicit calculations
for complements to arrangements are made.
A. Libgober was supported by National Science Foundation grant. 相似文献
3.
LU Wenxuan Department of Mathematics Tsinghua University Beijing China 《中国科学A辑(英文版)》2006,49(1):54-65
Hodge integrals over moduli spaces of curves appear naturally during the localization procedure in computation of Gromov-Witten invariants. A remarkable formula of Marino-Vafa expresses a generation function of Hodge integrals via some combinatorial and algebraic data seemingly unrelated to these apriori algebraic geometric objects. We prove in this paper by directly expanding the formula and estimating the involved terms carefully that except a specific type all the other Hodge integrals involving up to three Hodge classes can be calculated from this formula. This implies that amazingly rich information about moduli spaces and Gromov-Witten invariants is encoded in this complicated formula. We also give some low genus examples which agree with the previous results in literature. Proofs and calculations are elementary as long as one accepts Mumford relations on the reductions of products of Hodge classes. 相似文献
4.
Exact bounds for the positions of the branch points for cyclic coverings of the p-adic projective line by Mumford curves are calculated in two ways. Firstly, by using Fumiharu Kato’s *-trees, and secondly
by giving explicit matrix representations of the Schottky groups corresponding to the Mumford curves above the projective
line through combinatorial group theory. 相似文献
5.
We construct a natural branch divisor for equidimensional projective morphisms where the domain has lci singularities and the target is nonsingular. The method involves generalizing a divisor construction of Mumford from sheaves to complexes. The construction is valid in flat families. The generalized branch divisor of a stable map to a nonsingular curve X yields a canonical morphism from the space of stable maps to a symmetric product of X. This branch morphism (together with virtual localization) is used to compute the Hurwitz numbers of covers of the projective line for all genera and degrees in terms of Hodge integrals. 相似文献
6.
《Mathematische Nachrichten》2017,290(17-18):2800-2814
A classical example of Mumford gives a generically non‐reduced component of the Hilbert scheme of smooth curves in such that a general element of the component is contained in a smooth cubic surface in . In this article we use techniques from Hodge theory to give further examples of such (generically non‐reduced) components of Hilbert schemes of smooth curves without any restriction on the degree of the surface containing it. As a byproduct we also obtain generically non‐reduced components of certain Hodge loci. 相似文献
7.
Summary. We consider the Maxwell equations in a domain with Lipschitz boundary and the boundary integral operator A occuring in the Calderón projector. We prove an inf-sup condition for A using a Hodge decomposition. We apply this to two types of boundary value problems: the exterior scattering problem by a perfectly conducting body, and the dielectric problem with two different materials in the interior and exterior domain. In both cases we obtain an equivalent boundary equation which has a unique solution. We then consider Galerkin discretizations with Raviart-Thomas spaces. We show that these spaces have discrete Hodge decompositions which are in some sense close to the continuous Hodge decomposition. This property allows us to prove quasioptimal convergence of the resulting boundary element methods.
Mathematics Subject Classification (2000):65N30 相似文献
8.
Let G be a simple graph with n vertices. The coloring complex Δ(G) was defined by Steingrímsson, and the homology of Δ(G) was shown to be nonzero only in dimension n−3 by Jonsson. Hanlon recently showed that the Eulerian idempotents provide a decomposition of the homology group Hn−3(Δ(G)) where the dimension of the jth component in the decomposition, , equals the absolute value of the coefficient of λj in the chromatic polynomial of G, χG(λ).Let H be a hypergraph with n vertices. In this paper, we define the coloring complex of a hypergraph, Δ(H), and show that the coefficient of λj in χH(λ) gives the Euler Characteristic of the jth Hodge subcomplex of the Hodge decomposition of Δ(H). We also examine conditions on a hypergraph, H, for which its Hodge subcomplexes are Cohen–Macaulay, and thus where the absolute value of the coefficient of λj in χH(λ) equals the dimension of the jth Hodge piece of the Hodge decomposition of Δ(H). We also note that the Euler Characteristic of the jth Hodge subcomplex of the Hodge decomposition of the intersection of coloring complexes is given by the coefficient of jth term in the associated chromatic polynomial. 相似文献
9.
Riemann Existence Theorems for Galois covers of Mumford curves by Mumford curves are stated and proven. As an application, all finite groups are realised as full automorphism groups of Mumford curves in characteristic zero. 相似文献
10.
Peter Jossen 《Inventiones Mathematicae》2014,195(2):393-439
We show that the statement analogous to the Mumford–Tate conjecture for Abelian varieties holds for 1-motives on unipotent parts. This is done by comparing the unipotent part of the associated Hodge group and the unipotent part of the image of the absolute Galois group with the unipotent part of the motivic fundamental group. 相似文献
11.
该文使用Hodge分解的方法, 给出了A -调和方程divA(x, u, u)=0具有非负障碍函数的障碍问题很弱解的局部正则性结果. 相似文献
12.
13.
We study the Hodge decomposition of L
1-(and measure-) differential forms over a compact manifold without boundary, giving positive results and counterexamples.
The theory is then applied to the relaxation and minimization, in cohomology classes, of convex functionals with linear growth.
This corresponds to a non-linear version of the Hodge theory, in the spirit of L. M. Sibner and R. J. Sibner [SS].
Received: 19 November 1997 / Revised version: 18 May 1998 相似文献
14.
The orientable cover of the moduli space of real genus zero algebraic curves with marked points is a compact aspherical manifold tiled by associahedra, which resolves the singularities of the space of phylogenetic trees. The resolution maps planar metric trees to their underlying abstract representatives, collapsing and folding an explicit geometric decomposition of the moduli space into cubes, endowing the resolving space with an interesting canonical pseudometric. Indeed, the given map can be reinterpreted as relating the real and the tropical versions of the Deligne–Knudsen–Mumford compactification of the moduli space of Riemann spheres. 相似文献
15.
16.
Fumiharu Kato 《manuscripta mathematica》2001,104(4):451-458
We discuss Mumford curves in the pencil on a Del Pezzo quintic surface constructed by Edge [Ed1]. The abstract group structures
of the normalizer of the corresponding Schottky groups are described, which give us some knowledges on Mumford loci in moduli
space of curves.
Received: 5 July 2000 / Accepted: 23 October 2000 相似文献
17.
Reuben Rabi 《manuscripta mathematica》2001,105(4):425-469
We construct certain extensions of Hodge structures using points on algebraic curves and study them. We also introduce and
use a related function theory which forms a genus g > 0 version of that of classical hyperlogarithms.
Received: 9 May 2000 / Revised version: 8 December 2000 相似文献
18.
A Mumford curve of genus g=5,6,7 or 8 over a non-Archimedean field ofcharacteristic p (such that if p=0, the residue field characteristic exceeds 5) has at most 12(g–1) automorphisms. In this paper, all curves that attain this bound and their automorphism groups (called of Lamé type) are explicitly determined. 相似文献
19.
20.
《代数通讯》2013,41(2):805-813
We give effective bounds on the higher Hilbert coefficients of finitely generated modules over Noetherian local rings (A, m) with respect to m-primary ideals, in terms of the multiplicity, dimension and the lengths of local cohomology modules. We similarly bound the Castelnuovo–Mumford regularity of the associated Rees modules. 相似文献