Commutative algebra : interactions with algebraic geometry : International Conference, Grenoble, France, July 9-13, 2001, Special Session at the Joint International Meeting of the American Mathematica

Contents.
Introduction.
List of talks and references to publications.
Linearization of local cohomology modules.
Multiplicity-free subvarieties of flag varieties.
Morita contexts, idempotents, and Hochschild cohomology "with applications to invariant rings".
Introduction.
1. Morita contexts.
2. The grade of the stable endomorphism ring.
3. Equivalences to the generalized Nakayama conjecture.
4. The comparison homomorphism for Hochschild cohomology.
5. Hochschild cohomology of Auslander contexts.
6. Invariant rings: The general case.
7. Invariant rings: The commutative case.
References.
Some applications of two dimensional complete ideals.
Generically finite morphisms and simultaneous resolution of singularities.
Two results on the number of generators.
When is a binomial ideal equal to a lattice ideal up to radical?.
Depth and amplitude for unbounded complexes.
On the ideal of minors of matrices of linear forms.
Surjectivity of multiplication and F-regularity of multigraded rings.
On the Ext-modules of ideals of Borel type.
Sums of linked tepli ideals.
Cartan involutiveness = Mumford regularity.
The Frobenius endomorphism and homological dimensions.
Characterization of some projective subschemes by locally free resolutions.
1. Introduction.
2. Preliminaries.
3. q-presentations.
4. Surjective-Buchsbaum modules.
5. Arithmetically Buchsbaum subschemes.
6. Quasi-Buchsbaum subschemes.
7. Surfaces in P4.
References.
On unique factorization in semigroups of complete ideals.
Modules with strange homological properties and Chebychev polynomials.
Notes on the behavior of the Ratliff-Rush filtration.
On symbolic powers of prime ideals.
Multiplicities and the number of generators of Cohen-Macaulay ideals.
Chains of integrally closed ideals.