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Erschienen in:
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2018 | OriginalPaper | Buchkapitel

Platonic Surfaces

verfasst von : Brenda Leticia De La Rosa-Navarro, Gioia Failla, Juan Bosco Frías-Medina, Mustapha Lahyane, Rosanna Utano

Erschienen in: Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics

Verlag: Springer International Publishing

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Abstract

We define the notion of Platonic surfaces. These are anticanonical smooth projective rational surfaces defined over any fixed algebraically closed field of arbitrary characteristic and having the projective plane as a minimal model with very nice geometric properties. We prove that their Cox rings are finitely generated. In particular, they are extremal and their effective monoids are finitely generated. Thus, these Platonic surfaces are built from points of the projective plane which are in good position. It is worth noting that not only their Picard number may be big but also an anticanonical divisor may have a very large number of irreducible components.

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Vorheriges Kapitel An Introduction to Resolution of Singularities via the Multiplicity
Nächstes Kapitel Coverings of Rational Ruled Normal Surfaces
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Metadaten
Titel
Platonic Surfaces
verfasst von
Brenda Leticia De La Rosa-Navarro
Gioia Failla
Juan Bosco Frías-Medina
Mustapha Lahyane
Rosanna Utano
Copyright-Jahr
2018
Buch
Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics

Print ISBN: 978-3-319-96826-1

Electronic ISBN: 978-3-319-96827-8

Copyright-Jahr: 2018

DOI
https://doi.org/10.1007/978-3-319-96827-8_12

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