D-modules on 1|1 Supercurves
Algebraic Geometry
2015-05-13 v1 High Energy Physics - Theory
Mathematical Physics
math.MP
Abstract
It is known that to every 1|1 dimensional supercurve X there is associated a dual supercurve \hat{X}, and a superdiagonal \Delta in their product. We establish that the categories of D-modules on X, \hat{X}, and \Delta are equivalent. This follows from a more general result about D-modules and purely odd submersions. The equivalences preserve tensor products, and take vector bundles to vector bundles. Line bundles with connection are studied, and examples are given where X is a superelliptic curve.
Cite
@article{arxiv.0908.1989,
title = {D-modules on 1|1 Supercurves},
author = {Mitchell J. Rothstein and Jeffrey M. Rabin},
journal= {arXiv preprint arXiv:0908.1989},
year = {2015}
}
Comments
18 pages