This volume contains 21 articles based on invited talks given at two international conferences held in France in 2001. Most of the papers are devoted to various problems of commutative algebra and their relation to properties of algebraic varieties. The book is suitable for graduate students and research mathematicians interested in commutative algebra and algebraic geometry.
Linearization of local cohomology modules by J. A. Montaner and S. Zarzuela Multiplicity-free subvarieties of flag varieties by M. Brion Morita contexts, idempotents, and Hochschild cohomology--with applications to invariant rings-- by R.-O. Buchweitz Some applications of two dimensional complete ideals by A. Campillo and S. Encinas Generically finite morphisms and simultaneous resolution of singularities by S. D. Cutkosky Two results on the number of generators by J. Elias When is a binomial ideal equation equal to a lattice ideal up to radical? by K. Eto Depth and amplitude for unbounded complexes by H.-B. Foxby and S. Iyengar On the ideal of minors of matrices of linear forms by A. Guerrieri and I. Swanson Surjectivity of multiplication and $F$-regularity of multigraded rings by M. Hashimoto On the Ext-modules of ideals of Borel type by J. Herzog, D. Popescu, and M. Vladoiu Sums of linked tepli ideals by M. R. Johnson Cartan involutiveness = Mumford regularity by B. Malgrange The Frobenius endomorphism and homological dimensions by C. Miller Characterization of some projective subschemes by locally free resolutions by U. Nagel On unique factorization in semigroups of complete ideals by O. Piltant Modules with strange homological properties and Chebychev polynomials by J.-E. Roos Notes on the behavior of the Ratliff-Rush filtration by M. E. Rossi and I. Swanson On symbolic powers of prime ideals by S. Sather-Wagstaff Multiplicities and the number of generators of Cohen-Macaulay ideals by W. V. Vasconcelos Chains of integrally closed ideals by K.-i. Watanabe.