Séminaire de Mathématique

The Hodge Locus

by Gregorio Baldi (IHES)

Europe/Paris
Amphithéâtre Léon Motchane (IHES)

Amphithéâtre Léon Motchane

IHES

Le Bois Marie 35, route de Chartres 91440 Bures-sur-Yvette
Description

Séminaire de géométrie arithmétique

I will report on a joint work with Klingler and Ullmo. Given a polarizable variation of Hodge structure on a smooth quasi projective variety S (e.g. the one associated to a family of pure motives over S), Cattani, Deligne and Kaplan proved that its Hodge locus (the locus of closed points of S where exceptional Hodge tensors appear) is a countable union of closed algebraic subvarieties of S. In this talk I will discuss when this Hodge locus is actually algebraic.

If time permits I will explain how a similar circle of ideas can be used to show the existence of a genus four curve of «Mumford’s type» (thus answering a question of Gross/Serre).

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IHES Covid-19 regulations:

- all the participants who will attend the event in person will have to keep their mask on in indoor spaces
and where the social distancing is not possible;
- speakers will be free to wear their mask or not at the moment of their talk if they feel more comfortable
without it;
- Up to 25 persons in the conference room, every participant will be asked to be able to provide a health pass
- Over 25 persons in the conference room, every participant will be asked to provide a health pass which will
be checked at the entrance of the conference room.

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Christophe Soulé et Jeanine Van Order

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