Real normalized differentials and Arbarello's conjecture
  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 $n$. 
I. Krichever
math.AG hep-th nlin.SI