Hilbert functions of Cox rings of del Pezzo surfaces

JOURNAL OF ALGEBRA

卷:480

Article

Park, Jinhyung¹  Won, Joonyeong² 

[1] Korea Inst Adv Study, Sch Math, 85 Hoegiro, Seoul 02455, South Korea

[2] Inst for Basic Sci Korea, Ctr Geometry & Phys, 77 Cheongam Ro, Pohang 37673, Gyeongbuk, South Korea

关键词: Del Pezzo surface;    Cox ring;    Syzygy;    Hilbert function;   

DOI  :  10.1016/j.jalgebra.2017.02.028

来源: Elsevier

【 摘 要 】

To study syzygies of the Cox rings of del Pezzo surfaces, we calculate important syzygetic invariants such as the Hilbert functions, the Green-Lazarsfeld indices, the projective dimensions, and the Castelnuovo-Mumford regularities. Using these computations as well as the natural multigrading structures by the Picard groups of del Pezzo surfaces and Weyl group actions on Picard lattices, we determine the Betti diagrams of the Cox rings of del Pezzo surfaces of degree at most four. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free