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Differentiability Of Volumes Of Divisors And A Problem Of Teissier
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2009 (English)In: Journal of Algebraic Geometry, ISSN 1056-3911, E-ISSN 1534-7486, Vol. 18, no 2, 279-308 p.Article in journal (Refereed) Published
Abstract [en]

We give an algebraic construction of the positive intersection products of pseudo-effective classes and use them to prove that the volume function on the Neron-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. We then 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.

Place, publisher, year, edition, pages
2009. Vol. 18, no 2, 279-308 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-32167ISI: 000264139800004Scopus ID: 2-s2.0-77952195411OAI: oai:DiVA.org:kth-32167DiVA: diva2:409354
Funder
Swedish Research Council
Note
QC 20110408Available from: 2011-04-08 Created: 2011-04-07 Last updated: 2017-12-11Bibliographically approved

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