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Algebra Seminar

The Kodaira dimension of some moduli spaces of elliptic K3 surfaces

Giacomo Mezzedimi (Hannover)

Date & time: Wednesday, 07 October 2020 at 2:00PM - 3:00PM

Abstract: Let \(\mathcal{M}_{2k}\) denote the moduli space of \(U\oplus \langle -2k\rangle\)-polarized K3 surfaces. Geometrically, the K3 surfaces in \(\mathcal{M}_{2k}\) are elliptic and contain an extra curve class, depending on \(k\ge 1\). I will report on a joint work with M. Fortuna and M. Hoff, in which we compute the Kodaira dimension of \(\mathcal{M}_{2k}\) for almost all \(k\): more precisely, we show that it is of general type if \(k\ge 220\) and unirational if \(k\le 50, k\) not in \( \{11,35,42,48\}\). After introducing the general problem, I will compare the strategies used to obtain both results. If time permits, I will show some examples arising from explicit geometric constructions.

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