We prove the finite generation of the monoid of effective divisor classes on a Platonic rational surface,then derive some consequences. We also show the vanishing of the irregularity of any numerically effective divisor, solving thus the Reimann-Roch Problem for numerically effective divisors. Platonic rational surfaces provide neew evidence to a speculationof Felix Klein about the interaction between geometry and discrete mathematics

The finite generation of the monoid of effective divisor classes on Platonic rational surfaces

FAILLA, Gioia;
2007

Abstract

We prove the finite generation of the monoid of effective divisor classes on a Platonic rational surface,then derive some consequences. We also show the vanishing of the irregularity of any numerically effective divisor, solving thus the Reimann-Roch Problem for numerically effective divisors. Platonic rational surfaces provide neew evidence to a speculationof Felix Klein about the interaction between geometry and discrete mathematics
9812704108
smooth rational surfaces; anticanonical divisor; blowing up
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/20.500.12318/16295
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? 4
social impact