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Séminaire de géométrie

École polytechnique  – Salle de conférences du Centre de Mathématiques Laurent Schwartz

Du fait de l'aggravation de la situation pandémique, les orateurs du séminaire de jeudi donneront leurs exposés à distance sur le lien Zoom ci-dessous.

Meeting ID: 856 2228 4141
Passcode: 215072


10h30-12h : Mihai Paun (Univ. Bayreuth)

"Extension of twisted canonical sections defined on infinitesimal neighborhoods of the central fiber of a Kaehler family"

Abstract: We will present a recent work in collaboration with J. Cao and Y. Deng, respectively. We start by discussing an elementary, direct proof a a well-known result concerning the structure of the so-called "Green-Lazarsfeld" sets. The second part of our talk concerns a general extension result for canonical forms defined on a infinitesimal neighborhood the central fiber of a Kaehler family. Our main techniques are partly relying on ideas introduced by M. Levine in the 80's, themselves originating in the work of H. Grauert. The main motivation for our results is a conjecture proposed by Y.-T. Siu in 2002, about invariance of plurigenera for Kaehler families.

14h-15h30 : Bo Berndtsson (Chalmers Univ.)

"Some remarks on long geodesics in the Mabuchi space of kahler metrics"

Abstract: This talk is about geodesics in the space of Kahler metrics that are defined for all time. Such curves are conjecturally induced by holomorphic vector fields, and we show that this is indeed so for regular geodesics, whereas the question for generalized geodesics is still open (as far as we know). We also give a result about the derivative of such geodesics which implies a variant of a theorem of Atiyah and Guillemin-Sternberg on convexity of the image of certain moment maps.