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Séminaire de Géométrie

École polytechnique – Centre de Mathématiques Laurent Schwartz

 

14h30 – Gergely BÉRCZI (Université d'Aarhus, Danemark)

"Enumerative geometry and hyperbolicity via non-reductive quotients"

Abstract: The starting point of this talk is the moduli of n-tuples of regular commuting nilpotent k-by-k matrices, which coincides with the curvilinear locus of the Hilbert scheme of k points on the affine n-space. It also coincides with the moduli of invariant jet differentials of Demailly, and can be described as a non-reductive quotient. 

We show how different projective compactifications of this moduli space lead, on one hand, to curve counts which generalise the classical Goettshe nodal curve counting formula, and on other hand, to effective degree bounds in the Kobayashi hyperbolicity conjecture for hypersurfaces.