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Weddle surfaces and 3-level moduli spaces of abelian surfaces
Michele Bolognesi
1.11.2005, 14:00 Uhr – 16:00 Uhr

It is well known that the threefold $ \mathcal{B}\subset\mathbb{P}^4$ known as the Bürkhardt quartic is deeply related to moduli spaces of abelian surfaces with some 3-level structure, in particular to $ \mathcal{A}_2(3)$ and $ \mathcal{A}_2(3,6)$ . We show another such relation with $ \mathcal{A}_2(3)^-$ , a moduli space that we introduce, parametrizing principally polarized abelian surfaces with a symmetric theta structure and the choice of an odd theta characteristic. We shall build the arithmetic group that defines $ \mathcal{A}_2(3)^-$ as a quotient of the Siegel half-space and prove that it is birational to $ \mathbb{P}^3$ thus giving a moduli interpretation to the classical unirationalization of $ \B$ given by Weddle quartics. We also investigate the relation between these quartics, Kummer surfaces and the Igusa quartic.

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Veranstaltungen 2005