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Jian Xiao

Teissier's problem on propotionality of nef classes over compact Kähler manifolds.
Lundi, 20 Octobre, 2014 - 10:30
Résumé : 

By establishing an analogue of Diskant's inequality in convex geometry for nef big divisors, Boucksom-Favre-Jonsson deduced a solution to a problem of Teissier on propotionality of nef line bundles on a complete algebraic variety over an algebraically closed field of characteristic zero. And Cutkosky extended their results to an arbitrary field. The algebro-geometric version of Diskant's inequality is strong enough to establish that equality in the Khovanskii-Teissier inequalities for nef big divisors holds iff the divisors are numerically propotional. We will resolve Teissier's propotionality problem for any transcendental nef classes (not only for line bundles) over compact Kähler manifolds directly, without using the transcendental version of Diskant's inequality which is unknown yet. Thus, for projective algebraic manifolds over $C$, this covers the previous results of Boucksom-Favre-Jonsson and Cutkosky.

Institution de l'orateur : 
Institut Fourier
Thème de recherche : 
Algèbre et géométries
Salle : 
4
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