Hodge classes on the moduli space of W(E6) covers and the geometry of A6

Elham Izadi

The Kodaira dimensions of moduli spaces of principally polarized abelian varieties are known except in the case of dimension 6. One approach to understanding the geometry of moduli spaces of abelian varieties is to parametrize them with suitable moduli spaces of curves. We proved earlier that principally polarized abelian sixfolds are Prym-Tjurin varieties of covers of P^1 with monodromy W(E6) and identified three divisors on the moduli space M(W(E6)) of W(E6) covers that are not contracted by the Prym-Tjurin map. Here we introduce naturally occurring divisors on M(W(E6)) obtained from the irreducible representations of W(E6). We compute these divisors in terms of the three main divisors and give a concrete description of the ramification divisor of the Prym-Tjurin map. We also give a second, more elementary, proof of the dominance of the Prym-Tjurin map. This is joint work with Alexeev, Donagi, Farkas, Ortega.

http://scgp.stonybrook.edu/video_portal/video.php?id=5651

Simons- Workshop: Birational Complexity of Algebraic Varieties