A Note on Quadratically Parametrized Surfaces  

作　　者：J. William Hoffman Haohao Wang 

机构地区：[1]Department of Mathematics, Louisiana State University Baton Rouge, Louisiana 70803, USA [2]Department of Mathematics, Southeast Missouri State University Cape Girardeau, MO 63701, USA

出　　处：《Algebra Colloquium》2014年第3期461-476,共16页代数集刊（英文版）

摘　　要：Let f0, f1, f2, f3 be linearly independent homogeneous quadratic forms in the standard Z-graded ring R ：= K[s, t, u], and gcd（f0, f1, f2, f3） = 1. This defines a rational map Ф ： P2 → P3. The Rees algebra Rees（I） = R I I2 … of the ideal I = （f0, fl, f2, fs） is the graded R-algebra which can be described as the image of an R-algebra homomorphism h ： R[x, y, z, w] → Rees（I）. This paper discusses the free resolutions of I, and the structure of ker（h）.Let f0, f1, f2, f3 be linearly independent homogeneous quadratic forms in the standard Z-graded ring R ：= K[s, t, u], and gcd（f0, f1, f2, f3） = 1. This defines a rational map Ф ： P2 → P3. The Rees algebra Rees（I） = R I I2 … of the ideal I = （f0, fl, f2, fs） is the graded R-algebra which can be described as the image of an R-algebra homomorphism h ： R[x, y, z, w] → Rees（I）. This paper discusses the free resolutions of I, and the structure of ker（h）.

关 键 词：Rees algebra SYZYGY local cohomology implicit equations 

分 类 号：O151.21[理学—数学] O484[理学—基础数学]