id: 05218468
dt: b
an: 05218468
au: Iyengar, Srikanth B.; Leuschke, Graham J.; Leykin, Anton; Miller, Claudia;
    Miller, Ezra; Singh, Anurag K.; Walther, Uli
ti: Twenty-four hours of local cohomology.
so: Graduate Studies in Mathematics 87. Providence, RI: American Mathematical
    Society (AMS) (ISBN 978-0-8218-4126-6/hbk). xviii, 282~p. \$~55.00
    (2007).
py: 2007
pu: Providence, RI: American Mathematical Society (AMS)
la: EN
cc: 
ut: 
ci: 
li: 
ab: This book is on local cohomology. It is explained how local cohomology is
    related to algebra, geometry, topology, combinatorics and computational
    algebra. The book consists of 24 chapters which are called lectures;
    each lecture has its own topic. The first few lectures present general
    (i.~e., quite independent from local cohomology) material from
    Commutative Algebra and Algebraic Geometry (to name a few, there are
    lectures on Krull dimension, tangent spaces, limits, Cohen-Macaulay
    rings, Gorenstein rings). An important subject which is also explained
    is the relation between local cohomology and the minimal number of
    defining equations of an algebraic set (the so-called arithmetic rank).
    In the subsequent lectures more sophisticated concepts are explained
    (e.~g. connectedness questions, $D$-modules, de Rham cohomology,
    duality theorems, relations between various notions of cohomology, but
    also polyhedra and algorithmic aspects of local cohomology).
rv: Michael Hellus (Leipzig)