Syzygies of Cox rings of del Pezzo surfaces

来源 :Algebraic geometry, number theory, and related topics(代数几何,数 | 被引量 : 0次 | 上传用户：fengk9000

【摘要】

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　　There has been considerable interest in understanding Cox rings of del Pezzo surfaces.The main problem was the Batyrev-Popov conjecture which describes the

【作者】

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Jinhyung Park

【出处】

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Algebraic geometry, number theory, and related topics(代数几何,数

【发表日期】

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2015年5期

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　　There has been considerable interest in understanding Cox rings of del Pezzo surfaces.The main problem was the Batyrev-Popov conjecture which describes the relations of generators of those rings,and Testa-Varilly-Alvarado-Velasco and Sturmfels-Xu independently verified this conjecture a few years ago.It is then natural to study syzygies of the relations.After showing basic properties of Cox rings of del Pezzo surfaces,some important invariants such as Hilbert functions,projective dimensions,and Castelnuovo-Mumford regularities are calculated.Based on this calculation,I give an alternative proof of the Batyrev-Popov conjecture and compute the graded betti numbers of Cox rings of some del Pezzo surfaces.This is joint work with Joonyeong Won.

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Syzygies of Cox rings of del Pezzo surfaces

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