Varieties of sums of powers and moduli spaces of(1, 7)-polarized abelian surfaces

Michele Bolognesi (1) , Alex Massarenti (2)

1 IMAG - Institut Montpelliérain Alexander Grothendieck
2 UFF - Universidade Federal Fluminense [Rio de Janeiro]

We study the geometry of some varieties of sums of powers related to the Klein quartic. This allows us to describe the birational geometry of certain moduli spaces of abelian surfaces. In particular we show that the moduli space of A$_{2}$(1,7)$^-_{sym}$ of (1,7)-polarized abelian surfaces with a symmetric theta structure and an odd theta characteristic is unirational by showing that it admits a dominant morphism from a unirational conic bundle.

Domaines: Géométrie algébrique [math.AG]; Théorie des nombres [math.NT]

Michele Bolognesi, Alex Massarenti. Varieties of sums of powers and moduli spaces of(1, 7)-polarized abelian surfaces. Journal of Geometry and Physics, 2018, 125, pp.23 - 32. ⟨10.1016/j.geomphys.2017.12.004⟩. ⟨hal-01816624⟩