Moduli spaces of (1,7)-polarized abelian surfaces and varieties of sums of powers

Michele Bolognesi, Alex Massarenti

Published 2017-04-23Version 1

We study the geometry of some varieties of sums of powers related to the Klein quartic. Thanks to preceding results of Mukai and of ourselves, this allows us to describe the birational geometry of certain moduli spaces of abelian surfaces. In particular we show that $\mathcal{A}_2(1,7)^{-}_{sym}$ is unirational by showing that it admits a dominant morphism from a conic bundle.