Moriwaki divisors and the augmented base loci of divisors on the moduli space of curves

  title={Moriwaki divisors and the augmented base loci of divisors on the moduli space of curves},
  author={Salvatore Cacciola and Angelo Felice Lopez and Filippo Viviani},
  journal={arXiv: Algebraic Geometry},
We study the cone of Moriwaki divisors on \bar{M}_g by means of augmented base loci. Using a result of Moriwaki, we prove that an R-divisor D satisfies the strict Moriwaki inequalities if and only if the augmented base locus of D is contained in the boundary of \bar{M}_g. Then we draw some interesting consequences on the Zariski decomposition of divisors on \bar{M}_g, on the minimal model program of \bar{M}_g and on the log canonical models \bar{M}_g(\alpha). 

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