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Examples of non-commutative Hodge structures

Part of: Families, fibrations

Published online by Cambridge University Press:  10 March 2011

Claus Hertling  and
Claude Sabbah
Claus Hertling
Affiliation:
Lehrstuhl für Mathematik VI, Universität Mannheim, Seminargebäude A 5, 6, 68131 Mannheim, Germany ([email protected])
Claude Sabbah
Affiliation:
UMR 7640 du CNRS, Centre de Mathématiques Laurent Schwartz, École polytechnique, 91128 Palaiseau cedex, France ([email protected])
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Abstract

We show that, under a condition called minimality, if the Stokes matrix of a connection with a pole of order two and no ramification gives rise, when added to its adjoint, to a positive semidefinite Hermitian form, then the associated integrable twistor structure (or TERP structure, or noncommutative Hodge structure) is pure and polarized.

Keywords

Hermitian pairingLaplace transformationmeromorphic connectionStokes matrixnon-commutative Hodge structure

MSC classification

Secondary: 14D07: Variation of Hodge structures
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 10 , Special Issue 3: A Special Issue in Honour of Louis Boutet de Monvel and Pierre Schapira , July 2011 , pp. 635 - 674
Copyright
Copyright © Cambridge University Press 2011

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