Seminario / Laza
SEMINARIO MATEMATICO E FISICO DI MILANO
AVVISO DI CONFERENZA
Venerdì 12 Luglio 2019, alle ore 14:30, presso la Sala Rappresentanza
(piano rialzato) del Dipartimento di Matematica dell'Università di Milano,
in Via Saldini 50
Prof. RADU LAZA
Stony Brook University
"The LLV decomposition for hyper-Kaehler cohomology"
Abstract: Looijenga—Lunts and Verbitsky (LLV) have shown that the cohomology of a compact hyper-Kaehler manifold admits the action of a big Lie algebra g, generalizing the usual sl(2) Hard Lefschetz action. We compute the LLV decomposition of the cohomology for the known classes of hyper-Kaehler manifolds (i.e. K3^n, Kim_n, OG6, and OG10). As an application, we easily recover the Hodge numbers of the exceptional example OG10. In a different direction, we establish the so-called Nagai’s conjecture (on the nilpotency index for higher degree monodromy operators) for the known cases. More interestingly, based on the known examples, we conjecture a new restriction on the cohomology of compact hyper-Kaehler manifolds, which in particular implies the vanishing of the odd cohomology as soon as the second Betti number is large enough relative to the dimension. This is joint work with M. Green, Y. Kim, and C. Robles.
Tutti gli interessati sono invitati a partecipare.
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