Selecta Mathematica

, Volume 16, Issue 2, pp 201–240 | Cite as

Vertex operators and the geometry of moduli spaces of framed torsion-free sheaves

  • Anthony Licata
  • Alistair SavageEmail author


We define complexes of vector bundles on products of moduli spaces of framed rank r torsion-free sheaves on \({\mathbb{P}^2}\) . The top non-vanishing equivariant Chern classes of the cohomology of these complexes yield actions of the r-colored Heisenberg and Clifford algebras on the equivariant cohomology of the moduli spaces. In this way we obtain a geometric realization of the boson-fermion correspondence and related vertex operators.

Mathematics Subject Classification (2000)

Primary 14C05 17B69 


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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  1. 1.Department of MathematicsStanford UniversityPalo AltoUSA
  2. 2.Department of Mathematics and StatisticsUniversity of OttawaOttawaCanada

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