Sagbi bases of Cox-Nagata rings

doi:10.4171/JEMS/204

	Sagbi bases of Cox-Nagata rings
	Sturmfels, Bernd 1; Xu, Zhiqiang2
	2010
发表期刊	JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY
ISSN	1435-9855
卷号	12 期号:2 页码:429-459
摘要	We degenerate Cox-Nagata rings to toric algebras by means of sagbi bases induced by configurations over the rational function field. For del Pezzo surfaces, this degeneration implies the Batyrev-Popov conjecture that these rings are presented by ideals of quadrics. For the blow-up of projective n-space at n + 3 points, sagbi bases of Cox-Nagata rings establish a link between the Verlinde formula and phylogenetic algebraic geometry, and we use this to answer questions due to D'Cruz-Iarrobino and Buczynska-Wisniewski. Inspired by the zonotopal algebras of Holtz and Ron, our study emphasizes explicit computations, and offers a new approach to Hilbert functions of fat points.
DOI	10.4171/JEMS/204
语种	英语
资助项目	Alexander von Humboldt ; U. S. National Science Foundation[DMS-0456960] ; Sofia Kovalevskaya prize awarded to Olga Holtz ; National Natural Science Foundation of China[10871196]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000275735300007
出版者	EUROPEAN MATHEMATICAL SOC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/9794
专题	计算数学与科学工程计算研究所
通讯作者	Sturmfels, Bernd
作者单位	1.Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA 2.Chinese Acad Sci, Inst Comput Math Acad Math & Syst Sci, LSEC, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Sturmfels, Bernd,Xu, Zhiqiang. Sagbi bases of Cox-Nagata rings[J]. JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY,2010,12(2):429-459.
APA	Sturmfels, Bernd,&Xu, Zhiqiang.(2010).Sagbi bases of Cox-Nagata rings.JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY,12(2),429-459.
MLA	Sturmfels, Bernd,et al."Sagbi bases of Cox-Nagata rings".JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY 12.2(2010):429-459.