Brill-Noether loci and the gonality stratification of {M_g}

Abstract

For an irreducible smooth projective complex curve C of genus g, the gonality defined as gon(C) = min{d ∈ Z≥1 : there exists a gd on C} is perhaps the second most natural invariant: it gives an indication of how far C is from being rational, in a way different from what the genus does. For g ≥ 3 we consider the stratification of the moduli space Mg of smooth curves of genus g given by gonality: Mg,2 ⊆ M 1 g,3 ⊆ . . . ⊆ M 1 g,k ⊆ . . . ⊆ Mg,