Perverse bundles and Calogero-Moser spaces

David Ben-Zvi, Thomas Nevins

Research output: Contribution to journalArticle

Abstract

We present a simple description of moduli spaces of torsion-free D-modules (D-bundles) on general smooth complex curves, generalizing the identification of the space of ideals in the Weyl algebra with CalogeroMoser quiver varieties. Namely, we show that the moduli of D-bundles form twisted cotangent bundles to moduli of torsion sheaves on X, answering a question of Ginzburg. The corresponding (untwisted) cotangent bundles are identified with moduli of perverse vector bundles on T*X, which contain as open subsets the moduli of framed torsion-free sheaves (the Hilbert schemes T *X[n] in the rank-one case). The proof is based on the description of the derived category of D-modules on X by a noncommutative version of the Beilinson transform on P1.

Original languageEnglish (US)
Pages (from-to)1403-1428
Number of pages26
JournalCompositio Mathematica
Volume144
Issue number6
DOIs
StatePublished - Nov 1 2008

Keywords

  • Calogero-Moser spaces
  • D-modules
  • Koszul duality
  • Perverse coherent sheaves

ASJC Scopus subject areas

  • Algebra and Number Theory

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