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. Dedicated to Professor Antonio Campillo-López (

Platonic Surfaces

FAILLA, Gioia
;
2018-01-01

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. Dedicated to Professor Antonio Campillo-López (
2018
978-3-319-96826-1
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12318/11892
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? ND
social impact