共查询到20条相似文献,搜索用时 15 毫秒
1.
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
2.
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
3.
Ehud De Shalit 《Israel Journal of Mathematics》1990,71(1):1-16
We define ap-adic analytic Hodge decomposition for the cohomology of Mumford curves, with values in a local system. When the local system
is trivial, we give a new proof of Gerritzen’s theorem, that this decomposition forms a variation of Hodge structure, in a
family of Mumford curves. 相似文献
4.
Christopher Deninger andAnnette Werner constructed a functor that associates representations of the algebraic fundamental group of an algebraic curve to a class of vector bundles on that curve. We compare this to a construction byFaltings for Mumford curves that associates representations of the Schottky group to semistable vector bundles of degree 0. We prove that for a certain class of vector bundles on Mumford curves the constructions induce isomorphic representations. 相似文献
5.
Karsten Kremer 《manuscripta mathematica》2010,133(1-2):83-103
An origami (also known as square-tiled surface) is a Riemann surface covering a torus with at most one branch point. Lifting two generators of the fundamental group of the punctured torus decomposes the surface into finitely many unit squares. By varying the complex structure of the torus one obtains easily accessible examples of Teichmüller curves in the moduli space of Riemann surfaces. The p-adic analogues of Riemann surfaces are Mumford curves. A p-adic origami is defined as a covering of Mumford curves with at most one branch point, where the bottom curve has genus one. A classification of all normal non-trivial p-adic origamis is presented and used to calculate some invariants. These can be used to describe p-adic origamis in terms of glueing squares. 相似文献
6.
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
7.
Robin de Jong 《Journal of Pure and Applied Algebra》2007,208(1):1-14
Using an explicit version of the Mumford isomorphism on the moduli space of hyperelliptic curves we derive a closed formula for the Arakelov-Green function of a hyperelliptic Riemann surface evaluated at its Weierstrass points. 相似文献
8.
《Journal of Pure and Applied Algebra》2001,155(2-3):93-103
This paper investigates the Castelnuovo–Mumford regularity of the generic hyperplane section of projective curves in positive characteristic, and yields an application to a sharp bound on the regularity for nondegenerate projective varieties. 相似文献
9.
The purpose of this paper is to explain and to generalize, in a homotopical way, the result of Barannikov–Kontsevich and Manin, which states that the underlying homology groups of some Batalin–Vilkovisky algebras carry a Frobenius manifold structure. To this extent, we first make the minimal model for the operad encoding BV-algebras explicit. Then, we prove a homotopy transfer theorem for the associated notion of homotopy BV-algebra. The final result provides an extension of the action of the homology of the Deligne–Mumford–Knudsen moduli space of genus 0 curves on the homology of some BV-algebras to an action via higher homotopical operations organized by the cohomology of the open moduli space of genus zero curves. Applications in Poisson geometry and Lie algebra cohomology and to the Mirror Symmetry conjecture are given. 相似文献
10.
Marco Pacini 《Geometriae Dedicata》2009,139(1):183-193
In [7], Mainò constructed a moduli space for enriched stable curves, by blowing-up the moduli space of Deligne–Mumford stable
curves. We introduce enriched spin curves, showing that a parameter space for these objects is obtained by blowing-up the
moduli space of spin curves.
The author was partially supported by CNPq (Proc.151610/2005-3) and by Faperj (Proc.E-26/152-629/2005). 相似文献
11.
We prove the existence of fine moduli spaces of simple coherent sheaves on families of irreducible curves. Our proof is based on the existence of a universal upper bound of the Castelnuovo–Mumford regularity of such sheaves, which we provide. 相似文献
12.
We give a bound on the Castelnuovo–Mumford regularity of a homogeneous ideal I, in a polynomial ring A, in terms of the number of variables and the degrees of generators, when the dimension of is at most two. This bound improves the one obtained by Caviglia and Sbarra in [G. Caviglia, E. Sbarra, Characteristic-free bounds for the Castelnuovo–Mumford regularity, Prépublication, math.AC/0310122]. In the continuation of the examples constructed in Chardin and D'Cruz [M. Chardin, C. D'Cruz, Castelnuovo–Mumford regularity: examples of curves and surface, J. Algebra 270 (2003) 347–360], we use families of monomial curves to construct homogeneous ideals showing that these bounds are quite sharp. To cite this article: M. Chardin, A.L. Fall, C. R. Acad. Sci. Paris, Ser. I 341 (2005). 相似文献
13.
We determine the Kodaira dimension of the Deligne–Mumford compactification \(\overline{\mathfrak{Diff }}_g\) of the universal difference variety over the moduli space of curves. 相似文献
14.
Amnon Besser 《Israel Journal of Mathematics》2006,151(1):53-59
We give a short proof of a formula of de Shalit, expressing the cup product of two vector-valued one-forms of the second kind
on a Mumford curve in terms of Coleman integrals and residues. The proof uses the notion of double indices on curves and their
reciprocity laws. 相似文献
15.
We extend some of the results of Carey-Marcolli-Rennie on modular index invariants of Mumford curves to the case of higher rank buildings. We discuss notions of KMS weights on buildings, that generalize the construction of graph weights over graph C*-algebras. 相似文献
16.
Damiano Fulghesu 《代数通讯》2013,41(8):2677-2700
This is the second in a series of three papers in which we investigate the rational Chow ring of the stack 𝔐0 consisting of nodal curves of genus 0. Here we define the basic classes: the classes of strata and the Mumford classes. 相似文献
17.
Lin Weng 《Mathematische Annalen》2001,320(2):239-283
In Part I, Deligne-Riemann-Roch isometry is generalized for punctured Riemann surfaces equipped with quasi-hyperbolic metrics.
This is achieved by proving the Mean Value Lemmas, which explicitly explain how metrized Deligne pairings for -admissible metrized line bundles depend on . In Part II, we first introduce several line bundles over Knudsen-Deligne-Mumford compactification of the moduli space (or
rather the algebraic stack) of stable N-pointed algebraic curves of genus g, which are rather natural and include Weil-Petersson, Takhtajan-Zograf and logarithmic Mumford line bundles. Then we use
Deligne-Riemann-Roch isomorphism and its metrized version (proved in Part I) to establish some fundamental relations among
these line bundles. Finally, we compute first Chern forms of the metrized Weil-Petersson, Takhtajan-Zograf and logarithmic
Mumford line bundles by using results of Wolpert and Takhtajan-Zograf, and show that the so-called Takhtajan-Zograf metric
on the moduli space is algebraic.
Received February 14, 2000 / Accepted August 18, 2000 / Published online February 5, 2001 相似文献
18.
Sabin Cautis 《Mathematische Annalen》2009,344(3):717-747
Necessary and sufficient conditions are given (in terms of monodromy) for extending a family of smooth curves over an open
subset to a family of stable curves over S. More precisely, we introduce the abelian monodromy extension (AME) property and show that the standard Deligne–Mumford compactification
is the unique, maximal AME compactification of the moduli space of curves. We also show that the Baily–Borel compactification
is the unique, maximal projective AME compactification of the moduli space of abelian varieties. 相似文献
19.
L. Gerritzen 《Israel Journal of Mathematics》1992,77(1-2):187-210
Mumford has studied the generalized Jacobian variety of a singular, irreducible curve in section 5 of his book (1984). It
is determined by a period matrix which is a symmetric matrix whose diagonal is zero. The problem to determine systems of equations
for the period matrices of totally degenerate curves is the analogue of the Schottky problem. An essentially complete solution
is given. 相似文献
20.
Christopher Daw 《Archiv der Mathematik》2012,98(5):433-440
In this paper we give a short proof of the André-Oort conjecture for products of modular curves under the Generalised Riemann
Hypothesis using only simple Galois-theoretic and geometric arguments. We believe this method represents a strategy for proving
the conjecture for a general Shimura variety under GRH without using ergodic theory. We also demonstrate a short proof of
the Manin–Mumford conjecture for Abelian varieties using similar arguments. 相似文献