Seshadri-type constants and Newton-Okounkov bodies for non-positive at infinity valuations of Hirzebruch surfaces
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2019
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| _version_ | 1866917656634851328 |
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| author | Galindo, Carlos Monserrat, Francisco Moreno-Ávila, Carlos-Jesús |
| author_facet | Galindo, Carlos Monserrat, Francisco Moreno-Ávila, Carlos-Jesús |
| contents | We consider flags $E_\bullet=\{X\supset E\supset \{q\}\}$, where $E$ is an exceptional divisor defining a non-positive at infinity divisorial valuation $ν_E$ of a Hirzebruch surface $\mathbb{F}_δ$ and $X$ the surface given by $ν_E,$ and determine an analogue of the Seshadri constant for pairs $(ν_E,D)$, $D$ being a big divisor on $\mathbb{F}_δ$. The main result is an explicit computation of the vertices of the Newton-Okounkov bodies of pairs $(E_\bullet,D)$ as above, showing that they are quadrilaterals or triangles and distinguishing one case from another. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1905_03531 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Seshadri-type constants and Newton-Okounkov bodies for non-positive at infinity valuations of Hirzebruch surfaces Galindo, Carlos Monserrat, Francisco Moreno-Ávila, Carlos-Jesús Algebraic Geometry 14C20, 14E15, 13A18 We consider flags $E_\bullet=\{X\supset E\supset \{q\}\}$, where $E$ is an exceptional divisor defining a non-positive at infinity divisorial valuation $ν_E$ of a Hirzebruch surface $\mathbb{F}_δ$ and $X$ the surface given by $ν_E,$ and determine an analogue of the Seshadri constant for pairs $(ν_E,D)$, $D$ being a big divisor on $\mathbb{F}_δ$. The main result is an explicit computation of the vertices of the Newton-Okounkov bodies of pairs $(E_\bullet,D)$ as above, showing that they are quadrilaterals or triangles and distinguishing one case from another. |
| title | Seshadri-type constants and Newton-Okounkov bodies for non-positive at infinity valuations of Hirzebruch surfaces |
| topic | Algebraic Geometry 14C20, 14E15, 13A18 |
| url | https://arxiv.org/abs/1905.03531 |