Middle multiplicative convolution and hypergeometric equations

Nicolas Martin (1)

1 CMLS - Centre de Mathématiques Laurent Schwartz

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 [DS13] and [Mar18a] in the additive case. Moreover, the main theorem gives a new proof of a result of Fedorov computing the Hodge invariants of hypergeometric equations.

Mots clés: D-modules; middle convolution; Hodge theory; hypergeometric equations; D-modules

Domaines: Géométrie algébrique [math.AG]

Nicolas Martin. Middle multiplicative convolution and hypergeometric equations. Journal of Singularities, 2021, 23, pp.194-204. ⟨10.5427/jsing.2021.23k⟩. ⟨hal-01878318v2⟩