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arXiv · 1507.05710

The uniformization of the moduli space of principally polarized abelian 6-folds

Valery Alexeev·Ron Donagi·Gavril Farkas·Elham Izadi·Angela Ortega
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Abstract

Starting from a beautiful idea of Kanev, we construct a uniformization of the moduli space A_6 of principally polarized abelian 6-folds in terms of curves and monodromy data. We show that the general ppav of dimension 6 is a Prym-Tyurin variety corresponding to a degree 27 cover of the projective line having monodromy the Weyl group of the E_6 lattice. Along the way, we establish numerous facts concerning the geometry of the Hurwitz space of such E_6-covers, including: (1) a proof that the canonical class of the Hurwitz space is big, (2) a concrete geometric description of the Hodge-Hurwitz eigenbundles with respect to the Kanev correspondence and (3) a description of the ramification divisor of the Prym-Tyurin map from the Hurwitz space to A_6 in the terms of syzygies of the Abel-Prym-Tyurin curve.

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Valery Alexeev, Ron Donagi, Gavril Farkas, Elham Izadi, Angela Ortega. 2015-07-21. The uniformization of the moduli space of principally polarized abelian 6-folds. https://arxiv.org/abs/1507.05710

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