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Séminaire de Géométrie Ergodique

Salle de conférences – Centre de Mathématiques Laurent Schwartz

10h30-11h30 – Mihai Aurel Fulger (EPFL)

"Seshadri constants for curves"

Abstract: The Seshadri constants for nef divisors at a point of projective varieties are a measure of local positivity for the divisor at the point. They have been extensively studied on surfaces for their connection to the Nagata conjecture on the nef cone of the projective plane blown-up at 10 or more very general points. We propose a different generalization of the surface case by defining Seshadri constants for movable curves on projective varieties. It maintains many of the properties present in the case of divisors.

 

11h45-12h45 – René Mboro (CMLS)

"On 2-cycles on cubic hypersurfaces and related birational invariants"

Abstract: Let X be a smooth cubic hypersurface of the projective space. In view of rationality questions for cubic 5-folds, we present some (sketch) of results on birational invariants of those hyper- surfaces, related to 2-cycles. The method we use for the analysis is to reduce to problems on 1-cycles on the variety of line F(X) of the cubic. We present also bounds for the group of 1-cycles of the variety of lines F(X) of (cubic) hypersurface X to be generated by lines.