Periods for irregular singular connections on surfaces

Details Periods for irregular singular connections on surfaces Periods for irregular singular connections on surfaces

2006-09-15

arxiv.org/abs/math/0609439v1

Mathematics

Algebraic Geometry

34 pages; will appear in Math. Annalen

Scientific paper

We define homology groups for flat irregular singular connections on surfaces and a pairing between these and the de Rham cohomology of the connection, generalizing work of S. Bloch and H. Enault in dimension one. Assuming a conjecture of C. Sabbah (known to be true if the rank of the vector bundle is at most 5), we prove perfectness of the pairing. We comment on certain new phenomena appearing in dimension two.

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