This work is based on the lectures presented at the International Conference of Commutative Algebra and Algebraic Geometry held in Messina, Italy. It discusses developments and advances in commutative algebra, algebraic geometry, and combinatorics - highlighting the theory of projective schemes, the geometry of curves, determinantal and stable ideals, and free resolutions.
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ISBN-13
978-0-8247-0567-1 (9780824705671)
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Schweitzer Klassifikation
Herausgeber*in
Universit?t Duisburg-Essen, Germany
Universita de Messina, Italy
On free complete intersections; on the number of ideals of finite colength; realizable sequences linked to the Hilbert function of a 0-dimensional projective scheme; lexsegment ideals in the exterior algebra; on the equations defining toric projective varieties; KRS and determinantal ideals; the Koszul complex in projective dimension 1; Grobner bases as characteristic sets; threefolds with degenerate secant variety - on a theorem of G. Scorza; the unirationality of all conic bundles implies the unirationality of the quartic threefold; Gaussian ideals and the Dedekind-Mertens lemma; depth formulas for certain graded modules associated to a filtration - a survey; extremal Betti numbers of lexsegment ideals; local monomialization; isomorphism of complexes and lifts; Weil divisors on rational normal scrolls; families of Wronksian correspondences; a note on Hodge's postulation formula for Schubert varieties; unimodular rows and subintegral extensions; on commutative FGS-rings with ascending condition on annihilators; Cohen-Macaulay F-injective homomorphisms; valuations of ideals, evolutions and the vanishing of cohomology groups; on integral schemes of vector fields; Robert Rings and Dutta multiplicities; Hilbert functions of squarefree Veronese rings; on the conductor of a surface at a point whose projectivized tangent cone is a generic union of lines; lifting problems for codimension two subvarieties in Pn border cases; rank two bundles and reflexive sheaves on P and corresponding curves - an overview; on the structure of ext groups of strongly stable ideals; an introduction to tight closure; Eisenbud-Goto inequality on Stanley-Reisner rings.
