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Title:
Cohomology and Combinatorics for Supertori
Speaker:
Abstract:
A supertorus (“elliptic supercurve”) of dimension 1|1 is a simple example showing that sheaf cohomology groups of supermanifolds are generally non-free modules over the ring of Grassmann constants. I will generalize this example to supertori of dimension 1|n, computing H0(X,O) and H1(X,O). These groups simply reflect combinatorial invariant-theoretic properties of Grassmann algebras, and exhibit Serre duality and Lefschetz properties. This is a first step toward a general theory of Abelian supervarieties and Jacobians of supercurves.
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