Platonic Surfaces

Brenda Leticia De La Rosa-Navarro (), Gioia Failla (), Juan Bosco Frías-Medina, Mustapha Lahyane () and Rosanna Utano ()
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Brenda Leticia De La Rosa-Navarro: Universidad Autónoma de Baja California, Facultad de Ciencias
Gioia Failla: Università Mediterranea di Reggio Calabria
Juan Bosco Frías-Medina: Universidad Nacional Autónoma de México. Área de la Investigación Científica. Circuito Exterior, Ciudad Universitaria, Instituto de Matemáticas
Mustapha Lahyane: Universidad Michoacana de San Nicolás de Hidalgo (UMSNH), Instituto de Física y Matemáticas (IFM)
Rosanna Utano: Università di Messina, Dipartimento di Scienze Matematiche e Informatiche. Scienze Fisiche e Scienze della Terra

A chapter in Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics, 2018, pp 319-342 from Springer

Abstract: 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.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-96827-8_12

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DOI: 10.1007/978-3-319-96827-8_12

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