Middle multiplicative convolution and hypergeometric equations

Nicolas Martin

Journal of Singularities
volume 23 (2021), 194-204

Received: 20 September 2018. Received in revised form: 26 July 2021.

DOI: 10.5427/jsing.2021.23k

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Abstract:

Using a relation due to Katz linking up additive and multiplicative convolutions, we make explicit the behaviour of some Hodge invariants by middle multiplicative convolution, following Dettweiler and Sabbah and our own previous work in the additive case. Moreover, the main theorem gives a new proof of a result of Fedorov computing the Hodge invariants of hypergeometric equations.

1991 Mathematical Subject Classification:

14D07, 32G20, 32S40

Key words and phrases:

D-modules, middle convolution, Hodge theory, hypergeometric equations

Author(s) information:

Nicolas Martin
Centre de mathématiques Laurent Schwartz
École polytechnique, Université Paris-Saclay
F-91128 Palaiseau cedex, France
email: nicolas.martin@polytechnique.edu