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Irreducibility of
−1-classes on anticanonical rational surfaces
and finite generation of the effective monoid
Mustapha Lahyane and Brian Harbourne |
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Vol. 218 (2005), No. 1, 101–114
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Abstract |
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We give necessary and sufficient conditions for a divisor class on smooth projective anticanonical rational surfaces to be the class of a smooth rational curve of self-intersection −1. We characterize smooth projective anticanonical rational surfaces for which the monoid of classes (modulo algebraic equivalence) of effective divisors is not finitely generated, extending results of Lahyane for the case of rational surfaces X with KX2 = 0. |
Milestones
Received: 27 August 2001
Revised: 27 February 2004
Published: 1 January 2005
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Authors |
| Mustapha Lahyane | |
| Departamento Álgebra, Geometría y
Topología Facultad de Ciencias Universidad de Valladolid C/ Prado de la Magdalena s/n E-47005 Valladolid Spain |
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| Brian Harbourne | |
| Department of Mathematics University of Nebraska Lincoln, NE 68588-0323 United States |
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| http://www.math.unl.edu/~bharbour | |
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