Algebraic solutions to Griffiths' Infinitesimal Periods Relations

par Philippe Eyssisieux (Institut Fourier)

jeudi 9 oct. 2025, 10:30 → 11:30 Europe/Paris

Griffiths'infinitesimal period relations is a complex algebraic pfaffian system on a generalized flag manifold X which is invariant under the automorphism group of  X.  This pfaffian system is given by an algebraic subbundle of the tangent bundle, called the horizontal tangent bundle, and its smooth solutions are the smooth submanifolds that are tangent everywhere to the horizontal tangent bundle (horizontal submanifolds).
 We construct  the Chow variety of cycles solutions to this pfaffian system (a cycle is a solution if the regular locus of each irreducible component is a smooth solution) and use it to retrieve a globalise Robles 'theorem on Maximal Variations of Hodge Structures. Actually it is convenient to place oneself in the rather general framework of exterior differential systems.
 Joint with Minseong Kim.