English

Effective divisors on $M_g$ and a counterexample to the Slope Conjecture

Algebraic Geometry 2007-05-23 v2

Abstract

We prove two statements on the slopes of effective divisors on the moduli space of stable curves of genus g: first that the Harris-Morrison Slope Conjecture fails for g=10 and second, that in order to compute the slope of the moduli space of curves for g\leq 23, one only has to consider the coefficients of the Hodge class and that of the boundary divisor \delta_0 in the expansion of the relevant divisors. We conjecture that the same statement holds in arbitrary genus.

Keywords

Cite

@article{arxiv.math/0209171,
  title  = {Effective divisors on $M_g$ and a counterexample to the Slope Conjecture},
  author = {Gavril Farkas and Mihnea Popa},
  journal= {arXiv preprint arXiv:math/0209171},
  year   = {2007}
}

Comments

7 pages, minor expository changes