Differentiability of volumes of divisors and a problem of Teissier

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

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Algebraic Geometry, 14C20 (Primary); 14E05, 52A40 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/137240

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0608260
 http://arxiv.org/abs/math/0608260

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arXiv