The effective monoids of the blow-ups of Hirzebruch surfaces at points in general position

Autor:	Juan Bosco Frías-Medina, Mustapha Lahyane
Rok vydání:	2020
Předmět:	Monoid Surface (mathematics) Pure mathematics Class (set theory) Mathematics::Algebraic Geometry Property (philosophy) General Mathematics Finitely-generated abelian group Algebra over a field General position Hirzebruch surface Mathematics
Zdroj:	Rendiconti del Circolo Matematico di Palermo Series 2. 70:167-197
ISSN:	1973-4409 0009-725X
Popis:	The aim of this work is to present the classification of the surfaces obtained as blow-up of a Hirzebruch surface at points in general position according to the finiteness of their effective monoids and to determine explicitly their minimal generating sets in these cases. Moreover, we present a decomposition for every effective class in some concrete cases. Also, we make a further study regarding the concepts of Harbourne–Hirschowitz surface and anticanonical orthogonal property. As an application of the later concept and the finiteness of the effective monoid, we obtain the classification of the surfaces obtained as blow-up of a Hirzebruch surface in points in general position which have finitely generated Cox rings.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::bce62c1212b1d3343701d96c1f073177 https://doi.org/10.1007/s12215-020-00489-3 Zobrazit plný text záznamu Full text from SpringerLink