Xavier ROULLEAU – K3 surfaces with compact rational polyhedral effective cone and Picard number larger than 2

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Date(s) - 10/03/2020
11 h 00 min - 12 h 00 min

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Nikulin and Vinberg classified K3 surfaces which have a compact rational polyhedral effective cone and Picard number $>2$. These surfaces have a finite automorphism group and no elliptic fibrations ; there are 8 families of such a surfaces.
The Nikulin-Vinberg classification is obtained by using the Torelli Theorem and by explicitly describing the Néron-Severi group of these surfaces.
In this talk, using their previous results, we will present a more geometric description and construction of these surfaces. In particular we give some explicit exemples, and in some case we discuss about the unirationality of their moduli spaces.


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