2013/12/08 by Pinaki Mondal, Mondal, Pinaki
Computer Science · Mathematics · #14C20 #14J26 #14M27 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1312.2168
openalex publication_date 2013/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study a class of rational surfaces (considered in [Campillo, Piltant and Reguera, 2005]) associated to curves with one place at infinity and explicitly describe generators of the Cox ring and global sections of line bundles on these surfaces. In particular, we show that their Cox rings are finitely generated, i.e. they are Mori dream spaces. We also compute their "global Zariski semigroups at infinity" (consisting of line bundles which have no base points `at infinity') and "global Enriques semigroups" (generated by closures of curves in C2). In particular, we show that the global Zariski semigroups at infinity and Enriques semigroups of surfaces corresponding to pencils which are equisingular at infinity are isomorphic, which answers a question of [Campillo, Piltant and Reguera-Lopez, 2002]. We also give an effective algorithm to determine if a (rational) surface `admits systems of numerical curvettes' (these surfaces were also considered in [Campillo, Piltant and Reguera, 2005]).