English

Differentiability of volumes of divisors and a problem of Teissier

Algebraic Geometry 2007-09-04 v2

Abstract

We give an algebraic construction of the positive products of pseudo-effective classes first introduced by Boucksom, Demailly, Paun and Peternell, and use them to prove that the volume function on the Neron-Severi space of a projective variety is (once) differentiable. The differential is expressed as a positive product; we also relate it to the restricted volumes introduced by Ein et al and by Takayama. Then we apply our differentiability result to prove an algebro-geometric version of the Diskant inequality in convex geometry, allowing us to characterize the equality case of the Khovanskii-Teissier inequalities for nef and big classes.

Keywords

Cite

@article{arxiv.math/0608260,
  title  = {Differentiability of volumes of divisors and a problem of Teissier},
  author = {Sebastien Boucksom and Charles Favre and Mattias Jonsson},
  journal= {arXiv preprint arXiv:math/0608260},
  year   = {2007}
}

Comments

28 pages. Final version. To appear in J. Alg. Geom