Ideals Generated by Quadratic Polynomials
Tigran Ananyan, Melvin Hochster · Mathematical Research Letters · 2012
Let R be a polynomial ring in N variables over an arbitrary field K and let I be an ideal of R generated by n polynomials of degree at most 2. We show that there is a bound on the projective dimension of R/I that depends only on n, and not on N .The proof depends on showing that if K is infinite and n is a positive integer, there exists a positive integer C(n), independent of N , such that any n forms of degree at most 2 in R are contained in a subring of R generated over K by at most