Hodge theory of the middle convolution

Michael Dettweiler (1) , Claude Sabbah (2)

1 Universität Bayreuth
2 CMLS - Centre de Mathématiques Laurent Schwartz

We compute the behaviour of Hodge data by tensor product with a unitary rank-one local system and middle convolution by a Kummer unitary rank-one local system for an irreducible variation of polarized complex Hodge structure on a punctured complex affine line. We give applications of these formulas to local systems with G_2-monodromy.

Domaines: Géométrie algébrique [math.AG]; Théorie des nombres [math.NT]

Michael Dettweiler, Claude Sabbah. Hodge theory of the middle convolution. Publications of the Research Institute for Mathematical Sciences, 2013, 49 (4), pp.761-800. ⟨10.4171/PRIMS/119⟩. ⟨hal-00816198⟩