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

 

parlerà su

 

"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.

 

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Il direttore del Seminario

Irene Sabadini

 

 

Per ulteriori informazioni sulle attività del seminario: 

http://www.mate.polimi.it/smf