Hypersphere arrangement and imaginary cycles for hypergeometric integrals. (English) Zbl 1258.32008

Aomoto, Kazuhiko

Terao, Hiroaki (ed.) et al., Arrangements of hyperplanes. Proceedings of the 2nd Mathematical Society of Japan-Seasonal Institute, MSJ-SI, Sapporo, Japan, August 1–13, 2009. Tokyo: Mathematical Society of Japan (ISBN 978-4-931469-67-9/hbk). Advanced Studies in Pure Mathematics 62, 1-26 (2012).

Summary: We construct imaginary cycles as Lefschetz cycles for hypergeometric integrals associated with a hypersphere arrangement and discuss the relation to the twisted rational de Rham cohomology. We also discuss this in degenerate cases where several hyperspheres contact with each other. We pose two geometric problems involved in it.
For the entire collection see [Zbl 1242.14003].

MSC:

32S22	Relations with arrangements of hyperplanes
14F40	de Rham cohomology and algebraic geometry
52C35	Arrangements of points, flats, hyperplanes (aspects of discrete geometry)

Keywords:

hypersphere arrangement; hypergeometric integrals; twisted de Rham cohomology