Global geometry of surfaces defined by non-positive and negative at infinity valuations
We consider plane divisorial valuations of Hirzebruch surfaces and introduce the concepts of non-positivity and negativity at infinity. We prove that the surfaces given by valuations of the last types have nice global and local geometric properties. Moreover, non-positive at infinity divisorial valu...
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| Tipo de recurso: | tesis doctoral |
| Estado: | Versión publicada |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | CBUC, CESCA |
| Repositorio: | TDR. Tesis Doctorales en Red |
| OAI Identifier: | oai:www.tdx.cat:10803/672247 |
| Acceso en línea: | http://hdl.handle.net/10803/672247 http://dx.doi.org/10.6035/14104.2021.725853 |
| Access Level: | acceso abierto |
| Palabra clave: | Non-positive at infinity valuations Rational surfaces Cone of curves Newton-Okounkov bodies Plane valuations Singularities Ciències naturals, químiques, físiques i matemàtiques 514 |
| Sumario: | We consider plane divisorial valuations of Hirzebruch surfaces and introduce the concepts of non-positivity and negativity at infinity. We prove that the surfaces given by valuations of the last types have nice global and local geometric properties. Moreover, non-positive at infinity divisorial valuations are those divisorial valuations of Hirzebruch surfaces providing rational surfaces with minimal generated cone of curves. Non-positivity and negativity at infinity are also extended to the class of real valuations of the projective plane and the Hirzebruch surfaces. Finally, we compute the Seshadri-type constants for pairs formed by a big divisor and a divisorial valuation of a Hirzebruch surface and obtain the vertices of the Newton-Okounkov bodies of pairs as above under the non-positivity at infinity property. |
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