arXiv math/01071942001-07math.AG

Triple Massey products on curves, Fay's trisecant identity and tangents to the canonical embedding

Alexander Polishchuk

备注：: latex, 16 pages, a misprint corrected, references updated

英文摘要：

We show that Fay's trisecant identity follows from the A_{infinity}-constraint between certain triple Massey products in the derived category of coherent sheaves on a curve. We also deduce the matrix analogue of this identity that can be conveniently formulated using quasideterminants of matrices with non-commuting entries. On the other hand, looking at more special triple Massey products we derive a formula for the tangent line to a canonically embedded curve at a given point.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Tropical spectral curves, Fay's trisecant identity, and generalized ultradiscrete Toda lattice

We study the generalized ultradiscrete periodic Toda lattice T(M,N) which has tropical spectral curve. We introduce a tropical analogue of Fay's trisecant identity, and apply it to construct a general solution to T(M,N).

2010-05-09math-phmath.AGmath.MP

A tropical analogue of Fay's trisecant identity and the ultra-discrete periodic Toda lattice

We introduce a tropical analogue of Fay's trisecant identity for a special family of hyperelliptic tropical curves. We apply it to obtain the general solution of the ultra-discrete Toda lattice with periodic boundary conditions in terms of the tropical Riemann's theta function.

2009-02-23math-phmath.AGmath.MP

A proof of the Trisecant Identity through the Fourier-Mukai transform

Using the technique of the Fourier-Mukai transform we give an explicit set of generators of the ideal defining an algebraic curve as a subscheme of its Jacobian. Essentially, these ideals are generated by the Fay's trisecant identities.

2010-11-09math.AG

Zero-pole interpolation for matrix meromorphic functions on a compact Riemann surface, and a matrix Fay trisecant identity

This paper presents a new approach to constructing a meromorphic bundle map between flat vector bundles over a compact Riemann surface having a prescribed Weil divisor (i.e., having prescribed zeros and poles with directional as well as multiplicity information included in the vector case). This new formalism unifies the earlier approach of Ball-Clancey (in the setting of trivial bundles over an abstract Riemann surface) with an earlier approach of the authors (where the Riemann surface was assumed to be the normalizing Riemann surface for an algebraic curve embedded in ${\bold C}^2$ with dete…

1999-02-08alg-geommath.AG

Fay恒等式的高阶退化及其在可积方程中的应用

Higher order degenerations of Fay's identities and applications to integrable equations

本文提出Fay三割线恒等式的高阶退化形式，并证明其可构造Schwarzian KP方程的解。

2023-01-14math-phmath.AGmath.MP

New degeneration of Fay's identity and its application to integrable systems

In this paper we prove a new degenerated version of Fay's trisecant identity. The new identity is applied to construct new algebro-geometric solutions of the multi-component nonlinear Schrödinger equation. This approach also provides an independent derivation of known algebro-geometric solutions to the Davey-Stewartson equations.

2011-04-13math-phmath.AGmath.MP

更多相关论文收起更多论文

Determinantal Characterization of Canonical Curves and Combinatorial Theta Identities

We characterize genus g canonical curves by the vanishing of combinatorial products of g+1 determinants of Brill-Noether matrices. This also implies the characterization of canonical curves in terms of (g-2)(g-3)/2 theta identities. A remarkable mechanism, based on a basis of H^0(K_C) expressed in terms of Szego kernels, reduces such identities to a simple rank condition for matrices whose entries are logarithmic derivatives of theta functions. Such a basis, together with the Fay trisecant identity, also leads to the solution of the question of expressing the determinant of Brill-Noether matri…

2012-01-13hep-thmath.AGmath.CO

Computational approach to the Schottky problem

We present a computational approach to the classical Schottky problem based on Fay's trisecant identity for genus $g\geq 4$. For a given Riemann matrix $\mathbb{B}\in\mathbb{H}^{g}$, the Fay identity establishes linear dependence of secants in the Kummer variety if and only if the Riemann matrix corresponds to a Jacobian variety as shown by Krichever. The theta functions in terms of which these secants are expressed depend on the Abel maps of four arbitrary points on a Riemann surface. However, there is no concept of an Abel map for general $\mathbb{B} \in \mathbb{H}^{g}$. To establish linear …

2023-03-27math-phmath.AGmath.MP

Linear relations among holomorphic quadratic differentials and induced Siegel's metric on M_g

We derive the explicit form of the (g-2)(g-3)/2 linearly independent relations among the products of pairs in a basis of holomorphic abelian differentials in the case of canonical curves of genus g greater than 3. It turns out that Petri's relations remarkably match in determinantal conditions. We explicitly express the volume form on the moduli space M_g of canonical curves induced by the Siegel metric, in terms of the period Riemann matrix only. By the Kodaira-Spencer map, the relations lead to an expression of the induced Siegel metric on M_g, that corresponds to the square of the Bergman r…

2007-02-21hep-thmath.AG