Real normalized differentials and Arbarello's conjecture

Abstract

Using meromorphic differentials with real periods, we prove Arbarello's conjecture: any compact complex cycle of dimension $g-n$ in the moduli space \M_g of smooth genus $g$ algebraic curves must intersect the locus of curves having a Weierstrass point of order at most $n$.Comment: Final version to appear in "Functional analysis and its applications