Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4597388 | Journal of Pure and Applied Algebra | 2008 | 10 Pages |
Abstract
Let a,b,c be linearly independent homogeneous polynomials in the standard Z-graded ring Râk[s,t] with the same degree d and no common divisors. This defines a morphism P1âP2. The Rees algebra Rees(I)=RâIâI2â⯠of the ideal I=ãa,b,cã is the graded R-algebra which can be described as the image of an R-algebra homomorphism h: R[x,y,z]âRees(I). This paper discusses one result concerning the structure of the kernel of the map h and its relation to the problem of finding the implicit equation of the image of the map given by a, b, c. In particular, we prove a conjecture of Hong, Simis and Vasconcelos. We also relate our results to the theory of adjoint curves and prove a special case of a conjecture of Cox.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
David Cox, J. William Hoffman, Haohao Wang,