On the degree of curves with prescribed multiplicities and bounded negativity
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866913340337422336 |
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| author | Galindo, Carlos Monserrat, Francisco Moreno-Ávila, Carlos-Jesús Pérez-Callejo, Elvira |
| author_facet | Galindo, Carlos Monserrat, Francisco Moreno-Ávila, Carlos-Jesús Pérez-Callejo, Elvira |
| contents | We provide a lower bound on the degree of curves of the projective plane $\mathbb{P}^2$ passing through the centers of a divisorial valuation $ν$ of $\mathbb{P}^2$ with prescribed multiplicities, and an upper bound for the Seshadri-type constant of $ν$, $\hatμ(ν)$, constant that is crucial in the Nagata-type valuative conjecture. We also give some results related to the bounded negativity conjecture concerning those rational surfaces having the projective plane as a relatively minimal model. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2105_01483 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On the degree of curves with prescribed multiplicities and bounded negativity Galindo, Carlos Monserrat, Francisco Moreno-Ávila, Carlos-Jesús Pérez-Callejo, Elvira Algebraic Geometry 14C20, 14E15, 13A18 We provide a lower bound on the degree of curves of the projective plane $\mathbb{P}^2$ passing through the centers of a divisorial valuation $ν$ of $\mathbb{P}^2$ with prescribed multiplicities, and an upper bound for the Seshadri-type constant of $ν$, $\hatμ(ν)$, constant that is crucial in the Nagata-type valuative conjecture. We also give some results related to the bounded negativity conjecture concerning those rational surfaces having the projective plane as a relatively minimal model. |
| title | On the degree of curves with prescribed multiplicities and bounded negativity |
| topic | Algebraic Geometry 14C20, 14E15, 13A18 |
| url | https://arxiv.org/abs/2105.01483 |