Algebraic intersection for hyperbolic surfaces

Abstract

We show that the algebraic intersection form of hyperbolic surfaces of genus $g$ has a minimum in the moduli space and that the minimum grows in the order $(\log g{)}^{-2}$ in terms of the genus. We also describe the asymptotic behavior of the algebraic intersection form in the moduli space as the homologically systolic length goes to zero.

33 pages, 4 figures. All comments are welcome!