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;
2007-01-01

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
2007
9812704108
smooth rational surfaces; anticanonical divisor; blowing up
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12318/16295
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