Supercurves and Their Duals
by Jeffrey RABIN (UCSD)
Abstract:
A supercurve is a supersymmetric generalization of a Riemann surface, or
algebraic curve.
Supercurves have applications to superstring perturbation theory and
supersymmetric integrable systems.
A supercurve M is part of a triple which also includes the dual supercurve
$\hat{M}$, whose points represent divisors on M, and the "superdiagonal"
$M_2$ in $M \times \hat{M}$.
For Riemann surfaces these three objects would coincide.
I will survey the generalization of some classical Riemann surface
theory to supercurves, including cohomology of supercurves, contour
integration of holomorphic differentials, and classification of line bundles,
concluding with some open problems.