<abstract xmlns="http://www.w3.org/1999/xhtml">We prove the finite generation of the monoid of effective divisor classes on a smooth projective rational surface X endowed with an anticanonical divisor such that all its irreducible components are of multiplicity one except one which has multiplicity two. In almost all cases, the self-intersection of a canonical divisor KX on X is strictly negative, hence - KX is neither ample nor numerically effective. In particular, X is not a Del Pezzo surface. Furthermore, it is shown that the first cohomology group of a numerically effective divisor vanishes; as a consequence, we determine the dimension of the complete linear system associated to any given divisor on X</abstract>

We prove the finite generation of the monoid of effective divisor classes on a smooth projective rational surface X endowed with an anticanonical divisor such that all its irreducible components are of multiplicity one except one which has multiplicity two. In almost all cases, the self-intersection of a canonical divisor KX on X is strictly negative, hence - KX is neither ample nor numerically effective. In particular, X is not a Del Pezzo surface. Furthermore, it is shown that the first cohomology group of a numerically effective divisor vanishes; as a consequence, we determine the dimension of the complete linear system associated to any given divisor on X

Rational Surfaces with Anticanonical Divisor not Reduced

Instituto de Física y Matemúticas (I.F.M.) Universidad Michoacana de San Nicolas de Hidalgo (U.M.S.N.H.) Edificio C-3, Ciudad Universitaria. C. P.58040 Morelia, Michoacan, Mexico

University of Reggio Calabria, DIIES, Via Graziella, Feo di Vito, Reggio Calabria, Italy

Instituto de Matemúaticas, Universidad Nacional Autúonoma de Múexico, Mexico, D.F., C.P.04510

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

{"article-title":"Rational Surfaces with Anticanonical Divisor not Reduced"}

We prove the finite generation of the monoid of effective divisor classes on a smooth projective rational surface X endowed with an anticanonical divisor such...

Rational Surfaces with Anticanonical Divisor not Reduced

Online veröffentlicht: 05. März 2014

Seitenbereich: 229 - 240

DOI: https://doi.org/10.2478/auom-2013-0055

Schlüsselwörter
Rational surfaces, Neron-Severi group, Blowing-up, Monoid of effective divisor classes

This content is open access.

Rational Surfaces with Anticanonical Divisor not Reduced

Online veröffentlicht: 05. März 2014

Seitenbereich: 229 - 240

DOI: https://doi.org/10.2478/auom-2013-0055

SchlüsselwörterRational surfaces, Neron-Severi group, Blowing-up, Monoid of effective divisor classes

This content is open access.

Schlüsselwörter
Rational surfaces, Neron-Severi group, Blowing-up, Monoid of effective divisor classes