Failla, Gioia and Lahyane, Mustapha and Molica Bisci, Giovanni (2006) *On the finite generation of the monoid of effective divisor classes on rational surfaces of type (n, m).* Atti della Accademia Peloritana dei Pericolanti - Classe di Scienze MM.FF.NN., LXXXIV (1). ISSN 1825-1242

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## Abstract

We prove that every projective rational surface of type (n, m) has only a finite number of (-1) curves and only a finite number of (-2) curves, where n and m are nonnegative integers satisfying the inequality mn-m-4n<0. As a consequence of this result, it follows the finite generation of the monoid of effective divisor classes on such surface. Thus giving in particular, a uniform proof of the classical results stating that the monoid of effective divisor classes on the surface obtained by blowing up the projective plane at points which are either all collinear or which are all on a conic is finitely generated.

Item Type: | Article |
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Subjects: | M.U.S. - Contributi Scientifici > 01 - Scienze matematiche e informatiche M.U.S. - Miscellanea > Atti Accademia Peloritana > Classe di Scienze Fisiche, Matematiche e Naturali |

Divisions: | UNSPECIFIED |

Depositing User: | Mr Nunzio FemminÃ² |

Date Deposited: | 25 Nov 2009 |

Last Modified: | 13 Apr 2010 13:15 |

URI: | http://cab.unime.it/mus/id/eprint/523 |

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