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arXiv · 2207.09229

On the additivity of Newton-Okounkov bodies

Robert Wilms
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Abstract

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.

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Robert Wilms. 2022-07-19. On the additivity of Newton-Okounkov bodies. https://doi.org/10.1007/s13366-025-00807-9

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