Moduli of abelian surfaces, symmetric theta structures and theta characteristics
نویسندگان
چکیده
منابع مشابه
Moduli Spaces of Abelian Surfaces : Compactification , Degenerations , and Theta Functions (
theory of Lie groups—but many geometric questions lead to non-standard problems which go beyond, or lie on the frontiers of, standard theory. Such questions arise both in reassuringly down-to-earth topics like the existence of constant mean curvature surfaces in R, and in more esoteric ones such as the use of harmonic maps into 'buildings', which have been exploited by Gromov and Schoen to obta...
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Theta characteristics appeared for the first time in the context of characteristic theory of odd and even theta functions in the papers of Göpel [Go] and Rosenhain [Ro] on Jacobi’s inversion formula for genus 2. They were initially considered in connection with Riemann’s bilinear addition relation between the degree two monomials in theta functions with characteristics. Later, in order to syste...
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We study the Verlinde bundles of generalized theta functions constructed from moduli spaces of sheaves over abelian surfaces. In degree 0, the splitting type of these bundles is expressed in terms of indecomposable semihomogeneous factors. Furthermore, Fourier-Mukai symmetries of the Verlinde bundles are found, consistently with strange duality. Along the way, a transformation formula for the t...
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The object of study here is the singular locus of the theta divisor Θ of a principally polarized abelian variety (X,Θ). The special case when (X,Θ) is the Jacobian of a curve C shows that this is meaningful: singularities of Θ are closely related to the existence of special linear systems on the curve C and for curves of genus g ≥ 4 the divisor Θ is always singular. But for the general principa...
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Abelian surfaces over C with a polarisation of type (1, t), t a positive integer, are parametrised by a coarse moduli space At which is a quasiprojective variety. In this paper we shall concentrate on the case where t is a prime p ≥ 5, and show that for p sufficiently large (in fact p ≥ 173) any algebraic compactification of Ap is of general type. A few results similar to this are already known...
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ژورنال
عنوان ژورنال: Commentarii Mathematici Helvetici
سال: 2016
ISSN: 0010-2571
DOI: 10.4171/cmh/396