On the additivity of Newton-Okounkov bodies
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866908780074106880 |
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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 |