Moduli of (1, 7)-Polarized Abelian Surfaces via Syzygies
Moduli of (1, 7)-Polarized Abelian Surfaces via Syzygies
We prove that the moduli space X(1,7) of (1,7)–polarized abelian surfaces with canonical level–structure is birational to the Fano 3–fold V22 of polar hexagons of the Klein quartic (7). In particular X(1,7) is rational and the birational map to ℙ3 is defined over ℚ. As a byproduct we obtain explicitely …