Joint Reductions, Tight Closure, and the Briançon-Skoda Theorem, II

2 3 Ju n 20 08 ON THE BRIANÇON - SKODA THEOREM ON A SINGULAR VARIETY

Let Z be a germ of a reduced analytic space of pure dimension. We provide an analytic proof of the uniform BriançonSkoda theorem for the local ring OZ ; a result which is previously proved by Huneke by algebraic methods. For ideals with few generators we also get some sharper results.

1 M ay 2 00 9 ON THE BRIANÇON - SKODA THEOREM ON A SINGULAR VARIETY

Let Z be a germ of a reduced analytic space of pure dimension. We provide an analytic proof of the uniform BriançonSkoda theorem for the local ring OZ ; a result which was previously proved by Huneke by algebraic methods. For ideals with few generators we also get much sharper results.

An analytic approach to Briançon-Skoda type theorems

The Briançon-Skoda theorem can be seen as an effective version of the Hilbert Nullstellensatz and gives a connection between size conditions on holomorphic functions and ideal membership. The size conditions are captured algebraically by the notion of integral closure of ideals. Many techniques have been applied to prove the Briançon-Skoda theorem and variations of it. The first proof by Brianç...

Tight Closure and the Kodaira Vanishing Theorem

A Generalization of Tight Closure and Multiplier Ideals

We introduce a new variant of tight closure associated to any fixed ideal a, which we call a-tight closure, and study various properties thereof. In our theory, the annihilator ideal τ(a) of all a-tight closure relations, which is a generalization of the test ideal in the usual tight closure theory, plays a particularly important role. We prove the correspondence of the ideal τ(a) and the multi...