Moduli spaces of framed sheaves on certain ruled surfaces over elliptic curves

Thomas A. Nevins

Research output: Contribution to journalArticlepeer-review

Abstract

Fix a ruled surface S obtained as the projective completion of a line bundle L on a complex elliptic curve C; we study the moduli problem of parametrizing certain pairs consisting of a sheaf ℰ on S and a map of ℰ to a fixed reference sheaf on S. We prove that the full moduli stack for this problem is representable by a scheme in some cases. Moreover, the moduli stack admits an action by the group C*, and we determine its fixed-point set, which leads to explicit formulas for the rational homology of the moduli space.

Original languageEnglish (US)
Pages (from-to)1117-1151
Number of pages35
JournalInternational Journal of Mathematics
Volume13
Issue number10
DOIs
StatePublished - Dec 2002

Keywords

  • Framed sheaves
  • Localization
  • Moduli spaces
  • Ruled surfaces

ASJC Scopus subject areas

  • Mathematics(all)

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