On the additivity of Newton-Okounkov bodies

Fuente: arXiv
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Main Author: Wilms, Robert
Format: Preprint
Published: 2022
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author Wilms, Robert
author_facet Wilms, Robert
contents We study the additivity of Newton-Okounkov bodies. Our main result states that on two-dimensional subcones of the ample cone the Newto-Okounkov body associated to an appropriate flag acts additively. We prove this by induction relying on the slice formula for Newton-Okounkov bodies. Moreover, we discuss a necessary condition for the additivity showing that our result is optimal in general situations. As an application, we deduce an inequality between intersection numbers of nef line bundles.
format Preprint
id arxiv_https___arxiv_org_abs_2207_09229
institution arXiv
publishDate 2022
record_format arxiv
spellingShingle On the additivity of Newton-Okounkov bodies
Wilms, Robert
Algebraic Geometry
14M25, 14C17, 52A39
We study the additivity of Newton-Okounkov bodies. Our main result states that on two-dimensional subcones of the ample cone the Newto-Okounkov body associated to an appropriate flag acts additively. We prove this by induction relying on the slice formula for Newton-Okounkov bodies. Moreover, we discuss a necessary condition for the additivity showing that our result is optimal in general situations. As an application, we deduce an inequality between intersection numbers of nef line bundles.
title On the additivity of Newton-Okounkov bodies
topic Algebraic Geometry
14M25, 14C17, 52A39
url https://arxiv.org/abs/2207.09229