European Mathematical Society - o. villamayor
https://euro-math-soc.eu/author/o-villamayor
enThree Lectures on Commutative Algebra
https://euro-math-soc.eu/review/three-lectures-commutative-algebra
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>This book contains lecture notes from the Winter School on Commutative Algebra and Applications held in 2006. The first lecture (by H. Brenner) contains a discussion of a geometrical approach to problems concerning tight closures. Problems treated here include the question of characterization of the tight closure of an ideal in a Noetherian domain over a field of positive characteristic and the question of whether the tight closures commute with localizations in these rings. Both questions have negative answers and the counter-example concludes this part of the book. However the core of the lecture is the understanding of tight closure under the properties of vector bundles on corresponding projective curves. Next, a positive answer to the first question is given for some particular cases. The second lecture (by J. Herzog) considers relations of various structures and monomial ideals in commutative free algebras naturally given by these structures. These chapters are devoted to various possibilities of shifting operation of simplicial complexes, discrete polymatroids, a variation of Dirac's theorem on chordal graphs and Cohen-Macaulay graphs. </p>
<p>The last lecture (by Orlando Villamayor) gives a quite detailed exposition of two important results in algebraic geometry proved by Hironaka: the desingularization and embedded principalization of ideals (both theorems are in characteristic zero). The original proofs were existence proofs; the proofs presented here are constructive. All the lectures suppose that the reader has some experience in commutative algebra or algebraic geometry. The first one requires knowledge of vector bundles and cohomology and the second one supposes the reader to be familiar with the basic concepts of commutative algebra including the Stanley-Reisner rings. This lecture, in general, seems to be written for readers working in algebraic geometry. The topics of these lectures are quite attractive and the work contains very recent results of the authors. Any reader with a good background in commutative algebra could find this book interesting.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">ppr</div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/h-brenner" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">h. brenner</a></li><li class="vocabulary-links field-item odd"><a href="/author/j-herzog" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">j. herzog</a></li><li class="vocabulary-links field-item even"><a href="/author/o-villamayor" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">o. villamayor</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/american-mathematical-society" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">american mathematical society</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2008</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">978-0-8218-4434-2 </div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">USD 39</div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/13-commutative-rings-and-algebras" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">13 Commutative rings and algebras</a></li></ul></span>Thu, 26 May 2011 16:29:27 +0000Anonymous39178 at https://euro-math-soc.eu