## 15 Citations

Local Numerical Equivalences and Okounkov Bodies in Higher Dimensions

- Mathematics
- 2018

We continue to explore the numerical nature of the Okounkov bodies focusing on the local behaviors near given points. More precisely, we show that the set of Okounkov bodies of a pseudoeffective…

Okounkov bodies associated to pseudoeffective divisors II

- Mathematics
- 2015

We first prove some basic properties of Okounkov bodies, and give a characterization of Nakayama and positive volume subvarieties of a pseudoeffective divisor in terms of Okounkov bodies. Next, we…

Infinitesimal Newton-Okounkov bodies and jet separation

- Mathematics
- 2015

In this paper we explore the connection between asymptotic base loci and Newton-Okounkov bodies associated to infinitesimal flags. Analogously to the surface case, we obtain complete…

Algebraic reverse Khovanskii--Teissier inequality via Okounkov bodies

- Mathematics
- 2021

Let X be a projective variety of dimension n over an algebraically closed field of arbitrary characteristic and let A,B,C be nef divisors on X. We show that for any integer 1 ≤ k ≤ n− 1, (B · A) · (A…

Extended Okounkov bodies and multi-point Seshadri constants

- Mathematics
- 2017

Based on the work of Okounkov, Lazarsfeld-Mustata and Kaveh-Khovanskii independently associated a convex body, called the Okounkov body, to a big divisor on a smooth projective variety with respect…

Okounkov bodies associated to abundant divisors and Iitaka fibrations

- Mathematics
- 2017

The aim of this paper is to study the Okounkov bodies associated to abundant divisors. First, we extend a result of Lazarsfeld-Musta\c{t}\u{a} and Jow to the valuative Okounkov bodies of abundant…

A generalization of Δ-genus for big divisors on projective varieties

- MathematicsCommunications in Algebra
- 2019

Abstract Let X be a complex projective variety, and let D be a big Cartier divisor on X. For this data, we define an invariant that refines the Δ-genus introduced by Fujita for nef and big divisors.…

Singular divisors and syzygies of polarized abelian threefolds

- Mathematics
- 2018

We provide numerical conditions for a polarized abelian threefold $(A,L)$ to have simple syzygies, in terms of property $(N_p)$ and the vanishing of Koszul cohomology groups $K_{p,1}$. We rely on a…

Slices of Okounkov bodies of big divisors on Mori dream spaces

- Mathematics
- 2016

The purpose of this paper is to study the slices of the Okounkov bodies of Mori dream spaces. First, we analyze all the slices of the Okounkov bodies of big divisors on Mori dream spaces associated…

## References

SHOWING 1-10 OF 28 REFERENCES

Okounkov bodies associated to pseudoeffective divisors II

- Mathematics
- 2015

We first prove some basic properties of Okounkov bodies, and give a characterization of Nakayama and positive volume subvarieties of a pseudoeffective divisor in terms of Okounkov bodies. Next, we…

Infinitesimal Newton-Okounkov bodies and jet separation

- Mathematics
- 2015

In this paper we explore the connection between asymptotic base loci and Newton-Okounkov bodies associated to infinitesimal flags. Analogously to the surface case, we obtain complete…

Okounkov bodies and Zariski decompositions on surfaces

- Mathematics
- 2016

The purpose of this paper is to investigate the close relation between Okounkov bodies and Zariski decompositions of pseudoeffective divisors on smooth projective surfaces. Firstly, we completely…

Convex Bodies Associated to Linear Series

- Mathematics
- 2008

In his work on log-concavity of multiplicities, Okounkov showed in passing that one could associate a convex body to a linear series on a projective variety, and then use convex geometry to study…

Numerical and enumerative results on Okounkov bodies

- Mathematics
- 2015

In this note we focus on three independent problems on Okounkov bodies for projective varieties. The main goal is to present a geometric version of the classical Fujita Approximation Theorem, a…

Newton-Okounkov bodies, semigroups of integral points, graded algebras and intersection theory

- Mathematics
- 2009

Generalizing the notion of Newton polytope, we define the Newton-Okounkov body, respectively, for semigroups of integral points, graded algebras, and linear series on varieties. We prove that any…

Functions on Okounkov bodies coming from geometric valuations (with an appendix by S\'ebastien Boucksom)

- Mathematics
- 2012

We study topological properties of functions on Okounkov bodies as introduced by Boucksom-Chen and Witt-Nystr\"om. We note that they are continuous over the whole Okounkov body whenever the body is…