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$A_{\infty}$-structures, Brill–Noether loci and the Fourier–Mukai transform

Published online by Cambridge University Press:  04 December 2007

A. Polishchuk
A. Polishchuk
Affiliation:
Department of Mathematics and Statistics, Boston University, 111 Cunnington~Street, Boston, MA 02215, [email protected]
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Abstract

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We use the $A_{\infty}$-formalism to study variation in cohomology spaces under formal deformations of coherent sheaves on projective varieties. As an application we describe formal neighborhoods of some singular points in twisted Brill–Noether loci in the moduli spaces of vector bundles on a curve. Another application is a computation of the Fourier–Mukai transform of some natural line bundles on symmetric powers of a curve.

Keywords

$A_{\infty}$-structureBrill–Noether lociFourier–Mukai transform14H51 (primary)14D1514H40 (secondary)
Type
Research Article
Information
Compositio Mathematica , Volume 140 , Issue 2 , March 2004 , pp. 459 - 481
Copyright
Foundation Compositio Mathematica 2004