A note on quadratically parametrized surfaces
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 φ: ℙ2→ ℙ3. The Rees algebra Rees(I)=R ⊕ I ⊕ I2⊕. of the ideal I= 〈f0,f1,f2,f3〉 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). © 2014 Academy of Mathematics and Systems Science, Chinese Academy of Sciences, and Suzhou University.
Publication Source (Journal or Book title)
Hoffman, J., & Wang, H. (2014). A note on quadratically parametrized surfaces. Algebra Colloquium, 21 (3), 461-476. https://doi.org/10.1142/S1005386714000406