Okounkov bodies and restricted volumes along very general curves

By Shin-Yao Jow. 2009

52 citations recorded by the source corpus.

Abstract Given a big divisor D on a normal complex projective variety X, we show that the restricted volume of D along a very general complete-intersection curve C ⊂ X can be read off from the Okounkov body of D with respect to an admissible flag containing C. From this we deduce that if two big divisors D 1 and D 2 on X have the same Okounkov body with respect to every admissible flag, then D 1 and D 2 are numerically equivalent.

Subfields: Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/ce60f33d657f970fd89ff549761f6f110d86e785

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In Computational Theory and Mathematics

1. Kiumars Kaveh
2. Askold Khovanskii
3. Chi Li
4. G'abor Sz'ekelyhidi
5. Megumi Harada

In Geometry and Topology

1. Kiumars Kaveh
2. Askold Khovanskii
3. Chi Li
4. Ghislain Fourier
5. P. Littelmann
6. G'abor Sz'ekelyhidi
7. Megumi Harada

Citations in the corpus

• K-stability of Fano varieties via admissible flags (2020, unknown): “Then for every s-tuple (1 ≤ s ≤ l) of integers a = (a1, · · · , as) ∈ Ns , following [28], we define”
• Newton-Okounkov bodies, semigroups of integral points, graded algebras and intersection theory (2009, methodology): “pers [Lazarsfeld-Mustata08] and [Kaveh-Khovanskii08-1]. Recently the Newton convex body (which LazarsfeldMustata call Okounkov body) has been explored and used in the papers [Yuan08], [Nystrom09] and [Jow09]. First we briefly discuss the results we need from [Kaveh-Khovanskii08-2] and then we will ex”