Membranes and Sheaves

  title={Membranes and Sheaves},
  author={Nikita A. Nekrasov and Andrei Yur'evich Okounkov},
Our goal in this paper is to discuss a conjectural correspondence between the enumerative geometry of curves in Calabi–Yau 5-folds Z and 1-dimensional sheaves on 3-folds X that are embedded in Z as fixed points of certain C×-actions. In both cases, the enumerative information is taken in equivariant K-theory, where the equivariance is with respect to all automorphisms of the problem. In Donaldson–Thomas theory, one sums over all Euler characteristics with a weight (−q)χ, where q is a parameter… CONTINUE READING

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