Periods for rank 1 irregular singular connections on surfaces

2005/05/23 by Marco Hien, Hien, Marco
Mathematics · #14F40 #25A20 #32C38 #32S40 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT) #math.AG #math.NT #msc:14F40 #msc:25A20 #msc:32C38 #msc:32S40

paper · pdf · doi:10.48550/arxiv.math/0505474

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)

openalex publication_date 2005/05/23 · arxiv created 2006/02/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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