Colloquium: Jean Fasel, University Joseph Fourier - Grenoble 1: "Complete intersections on smooth affine varieties”


Let X=Spec(R) be a smooth affine variety and let Y be a closed subvariety corresponding to an ideal I in R. Finding a set of generators for I is in general a very hard problem, even in the case where X is an affine space over a field k. However, an easy application of Nakayama’s lemma shows that the number n of generators of I is at least the number m of generators of its conormal bundle and at most m+1. We will show how to actually determine when n=m using homotopical and cohomological methods, answering in particular a long standing conjecture of Murthy.

Coffee/Tea/Biscuit from 14.00

Published Feb. 15, 2016 8:35 AM - Last modified Feb. 15, 2016 8:35 AM