A Note on Quadratically Parametrized Surfaces

• 作者: Haohao Wang J. William Hoffman
• 来源期刊: 代数集刊:英文版
• 学科: 数学
• 关键词: 参数化 二次型 表面 代数同态 线性独立 F2 GCD 齐次
• 年，卷（期）: 2014,（3）
• 页码范围: 461-476
• 页数: 16页
• 分类号: O151.21
• 语种: 中文

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).