QUATERNION RATIONAL SURFACES

doi:10.1216/jca.2020.12.237

	QUATERNION RATIONAL SURFACES
	Hoffman, Jerome William 2; Jia, Xiaohong 1; Wang, Haohao 3
刊名	JOURNAL OF COMMUTATIVE ALGEBRA
	2020-06-01
卷号	12 期号:2 页码:237-261
关键词	syzygy graded minimal free resolution implicit equations
ISSN号	1939-0807
DOI	10.1216/jca.2020.12.237
英文摘要	A quaternion rational surface is a rational surface generated by two rational space curves via quaternion multiplication. In general, the structure of the graded minimal free resolution of a rational surface is unknown. The goal of this paper is to construct the graded minimal free resolution of a quaternion rational surface generated by two rational space curves. We will provide the explicit formulas for the maps of these graded minimal free resolutions. The approach we take is to utilize the information of the mu-bases of the generating rational curves, and create the generating sets for the first and second syzygy modules in the graded minimal free resolutions. In addition, we show that the ideal generated by the first syzygy module expressed in terms of moving planes is exactly the same as the ideal generated by the parametrization in the affine ring.
WOS研究方向	Mathematics
语种	英语
出版者	ROCKY MT MATH CONSORTIUM
WOS记录号	WOS:000538166200006
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/51551]
专题	中国科学院数学与系统科学研究院
通讯作者	Hoffman, Jerome William
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Natl Ctr Math & Interdisciplinary Sci, Beijing, Peoples R China 2.Louisiana State Univ, Dept Math, Baton Rouge, LA 70803 USA 3.Southeast Missouri State Univ, Dept Math, Cape Girardeau, MO 63701 USA
推荐引用方式 GB/T 7714	Hoffman, Jerome William,Jia, Xiaohong,Wang, Haohao. QUATERNION RATIONAL SURFACES[J]. JOURNAL OF COMMUTATIVE ALGEBRA,2020,12(2):237-261.
APA	Hoffman, Jerome William,Jia, Xiaohong,&Wang, Haohao.(2020).QUATERNION RATIONAL SURFACES.JOURNAL OF COMMUTATIVE ALGEBRA,12(2),237-261.
MLA	Hoffman, Jerome William,et al."QUATERNION RATIONAL SURFACES".JOURNAL OF COMMUTATIVE ALGEBRA 12.2(2020):237-261.