Periods for rank 1 irregular singular connections on surfaces
Algebraic Geometry
2007-05-23 v3 Number Theory
Abstract
We define a period pairing for flat, irregular singular, rank one connections, satisfying a technical condition regarding its stationary set, on complex surfaces between de Rham cohomology of the connection and a modified singular homology, the rapid decay homology. We prove that this gives a perfect duality. A 2-dimensional version of confluent hypergeometrics are contructed as an example.
Cite
@article{arxiv.math/0505474,
title = {Periods for rank 1 irregular singular connections on surfaces},
author = {Marco Hien},
journal= {arXiv preprint arXiv:math/0505474},
year = {2007}
}
Comments
28 pages; previous version partly incorrect (for higher rank case), new version contains case of line bundles and a new example. v3: technical assumption inserted (Definition 1.1)