1. The effective monoids of some blow-ups of Hirzebruch surfaces.
- Author
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Andablo-Reyes, G., De La Rosa-Navarro, B. L., and Lahyane, M.
- Subjects
- *
MONOIDS , *MATHEMATICS - Abstract
We mainly give a numerical condition to ensure the finite generation of the effective monoids of some smooth projective rational surfaces. These surfaces are constructed from the blow-up of any fixed Hirzebruch surface at some special configurations of ordinary points. Under this numerical condition, we determine explicitly the list of all (- 1) and (- 2) -curves. In particular, we complete a result obtained by Harbourne (Duke Math J 52(1):129–148, 1985) and another result obtained by the third author (C R Math 338(11):873–878, 2004). Moreover, the Cox rings of these surfaces are finitely generated. Our ground field is assumed to be algebraically closed of any characteristic. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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