03785nam a2200553 i 4500991003634529707536m o d cr nn||||mamaa190402s2018 sz a ob 000 0 eng d331975565X(eBook)9783319755656(eBook)3319755641(print)9783319755649(print)10.1007/978-3-319-75565-6doib14363604-39ule_instBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematicaeng516.35AMS 14-06LC QA251.3Commutative algebra and its interactions to algebraic geometry[e-book] :VIASM 2013-2014 /Nguyen Tu Cuong, Le Tuan Hoa, Ngo Viet Trung, editorsCham, Switzerland :Springer,[2018]1 online resource (ix, 256 pages) :illustrationstexttxtrdacontentcomputercrdamediaonline resourcecrrdacarriertext filePDFrdaLecture notes in mathematics,0075-8434 ;2210Includes bibliographical referencesNotes on Weyl algebra and D-modules / Markus Brodmann. Inverse systems of local rings / Juan Elias. Lectures on the representation type of a projective variety / Rosa M. Miró-Roig. Simplicial toric varieties which are set-theoretic complete intersections / Marcel Morales"This book presents four lectures on recent research in commutative algebra and its applications to algebraic geometry. Aimed at researchers and graduate students with an advanced background in algebra, these lectures were given during the Commutative Algebra program held at the Vietnam Institute of Advanced Study in Mathematics in the winter semester 2013 -2014. The first lecture is on Weyl algebras (certain rings of differential operators) and their D-modules, relating non-commutative and commutative algebra to algebraic geometry and analysis in a very appealing way. The second lecture concerns local systems, their homological origin, and applications to the classification of Artinian Gorenstein rings and the computation of their invariants. The third lecture is on the representation type of projective varieties and the classification of arithmetically Cohen-Macaulay bundles and Ulrich bundles. Related topics such as moduli spaces of sheaves, liaison theory, minimal resolutions, and Hilbert schemes of points are also covered. The last lecture addresses a classical problem: how many equations are needed to define an algebraic variety set-theoretically? It systematically covers (and improves) recent results for the case of toric varieties"--Print version, page 4 of coverAssociative ringsCommutative algebraCommutative ringsDifferential equations, PartialGeometry, AlgebraicBrodmann, Markus P.Cuong, Nguyen Tuauthorhttp://id.loc.gov/vocabulary/relators/aut785934Elias, JuanHoa, Le Tuanauthorhttp://id.loc.gov/vocabulary/relators/aut785935Miró-Roig, Rosa M.Morales Ibarra, MarcelTrung, Ngo VietPrint version:Commutative algebra and its interactions to algebraic geometry.Cham, Switzerland : Springer, [2018]9783319755649An electronic book accessile through the World Wide Webhttp://link.springer.com/10.1007/978-3-319-75565-6.b1436360403-03-2202-04-19991003634529707536Commutative algebra and its interactions to algebraic geometry1749870UNISALENTOle01302-04-19m@ -engsz 00