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1 results

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

  • A. Polishchuk
  • Journal:
    Compositio Mathematica / Volume 140 / Issue 2 / March 2004
    Published online by Cambridge University Press:
    04 December 2007, pp. 459-481
    Print publication:
    March 2004
    • Article
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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.