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<p>We study the additivity of Newton–Okounkov bodies. Our main result states that on two-dimensional subcones of the ample cone the Newton–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.</p>

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On the additivity of Newton–Okounkov bodies

  • 期刊论文

  • 发表日期：

    2025年9月6日

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  • Robert Wilms

摘要

We study the additivity of Newton–Okounkov bodies. Our main result states that on two-dimensional subcones of the ample cone the Newton–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.