A mathematical theory of quantum sheaf cohomology

Ron Donagi, Josh Guffin, Sheldon Katz, Eric Sharpe

Research output: Contribution to journalArticlepeer-review


The purpose of this paper is to present a mathematical theory of the half-twisted (0, 2) gauged linear sigma model and its correlation functions that agrees with and extends results from physics. The theory is associated to a smooth projective toric variety X and a deformation ε of its tangent bundle TX. It gives a quantum deformation of the cohomology ring of the exterior algebra of ε*. We prove that in the general case, the correlation functions are independent of 'nonlinear' deformations. We derive quantum sheaf cohomology relations that correctly specialize to the ordinary quantum cohomology relations described by Batyrev in the special case ε = TX.

Original languageEnglish (US)
Pages (from-to)387-418
Number of pages32
JournalAsian Journal of Mathematics
Issue number3
StatePublished - 2014


  • Gauged linear sigma model
  • Primitive collection
  • Quantum cohomology
  • Quantum shear cohomology
  • Toric varieties

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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