Commutative Algebra and its Interactions A conference in honor of Mel Hochster July 31 - August 5, 2008 Abstract Detail   Title: Tight closure is the better idea(l) Generic degree bounds for inclusion to tight closure. One of the standard features of tight closure theory is that theorems for regular rings, which express a containment to an ideal, can be generalized to arbitrary rings if we replace the ideal by its tight closure. The Briancon-Skoda theorem is a typical example. In this talk we are interested in standard-graded rings and the situation where a degree tuple is fixed. What elements of what degree do belong to the tight closure of an ideal generated by generically chosen elements of this degree tuple. This question is non trivial for polynomial rings, where it is directly related to the Froeberg conjecture, which is known in dimension three. We show how generic degree bounds on the polynomial ring imply generic degree bounds for tight closure in an arbitrary standard-graded ring. Surprisingly or not, the degree bounds do not depend on the rings, showing that tight closure of generic ideals behaves nicer that ideals themselves. This is joint work with Helena Fischbacher-Weitz. Holger Brenner University Osnabrück Email:  hbrenner@uni-osnabrueck.de Phone:   BACK to Speaker Listing BACK to Conference Home