Rational surfaces with finitely generated Cox rings and very high Picard numbers

被引：0
作者：
Brenda Leticia De La Rosa-Navarro
Juan Bosco Frías-Medina
Mustapha Lahyane
机构：
[1] Universidad Autónoma de Baja California,Facultad de Ciencias
[2] Universidad Michoacana de San Nicolás de Hidalgo (UMSNH) Edificio C-3,Instituto de Física y Matemáticas (IFM)
[3] Ciudad Universitaria,undefined
来源：
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas | 2017年 / 111卷
关键词：
Cox rings; Rational surfaces; Anticanonical Iitaka dimension; Effective monoid; Geometrically ruled surfaces ; Blowing-up; Primary 14C20; 14C22; 14J26; Secondary 14C17; 14E30; 14Q20;
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学科分类号：
摘要：
In this paper, we provide new families of smooth projective rational surfaces whose Cox rings are finitely generated. These surfaces are constructed by blowing-up points in Hirzebruch surfaces and may have very high Picard numbers. Such construction is not straightforward, and we achieve our results using the facts that these surfaces are extremal, and their effective monoids are finitely generated. Furthermore, we give an example illustrating the existence of rational surfaces which are not extremal. The base field of our varieties is assumed to be algebraically closed of arbitrary characteristic.
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页码：297 / 306
页数：9
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