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Article Dans Une Revue Journal of Algebraic Geometry Année : 2009

Differentiability of volumes of divisors and a problem of Teissier

Résumé

We give an algebraic construction of the positive intersection products of pseudo-effective classes first introduced in [BDPP], and use them to prove that the volume function on the Néron-Severi space of a projective variety is C 1-differentiable, expressing its differential as a positive intersection product. We also relate the differential to the restricted volumes introduced in [ELMNP3, Ta]. We then apply our dif-ferentiability 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.
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Dates et versions

hal-02105201 , version 1 (20-04-2019)

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Sébastien Boucksom, Charles Favre, Mattias Jonsson. Differentiability of volumes of divisors and a problem of Teissier. Journal of Algebraic Geometry, 2009, 18 (2), pp.279-308. ⟨10.1090/S1056-3911-08-00490-6⟩. ⟨hal-02105201⟩
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