LEADER 04243nam 22006975 450 001 9910300130403321 005 20200701232938.0 010 $a3-319-75565-X 024 7 $a10.1007/978-3-319-75565-6 035 $a(CKB)4100000005471796 035 $a(DE-He213)978-3-319-75565-6 035 $a(MiAaPQ)EBC6302748 035 $a(PPN)22991585X 035 $a(EXLCZ)994100000005471796 100 $a20180802d2018 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aCommutative Algebra and its Interactions to Algebraic Geometry$b[electronic resource] $eVIASM 2013?2014 /$fedited by Nguyen Tu CUONG, Le Tuan HOA, Ngo Viet TRUNG 205 $a1st ed. 2018. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2018. 215 $a1 online resource (IX, 258 p. 17 illus., 1 illus. in color.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2210 311 $a3-319-75564-1 320 $aIncludes bibliographical references. 327 $a1. Notes on Weyl Algebras and D-modules -- 2. Inverse Systems of Local Rings -- 3. Lectures on the Representation Type of a Projective Variety -- 4. Simplicial Toric Varieties which are set-theoretic Complete Intersections. 330 $aThis book presents four lectures on recent research in commutative algebra and its applications to algebraic geometry. Aimed at researchers and graduate students with an advanced background in algebra, these lectures were given during the Commutative Algebra program held at the Vietnam Institute of Advanced Study in Mathematics in the winter semester 2013 -2014. The first lecture is on Weyl algebras (certain rings of differential operators) and their D-modules, relating non-commutative and commutative algebra to algebraic geometry and analysis in a very appealing way. The second lecture concerns local systems, their homological origin, and applications to the classification of Artinian Gorenstein rings and the computation of their invariants. The third lecture is on the representation type of projective varieties and the classification of arithmetically Cohen -Macaulay bundles and Ulrich bundles. Related topics such as moduli spaces of sheaves, liaison theory, minimal resolutions, and Hilbert schemes of points are also covered. The last lecture addresses a classical problem: how many equations are needed to define an algebraic variety set-theoretically? It systematically covers (and improves) recent results for the case of toric varieties. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v2210 606 $aCommutative algebra 606 $aCommutative rings 606 $aAlgebraic geometry 606 $aAssociative rings 606 $aRings (Algebra) 606 $aPartial differential equations 606 $aCommutative Rings and Algebras$3https://scigraph.springernature.com/ontologies/product-market-codes/M11043 606 $aAlgebraic Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M11019 606 $aAssociative Rings and Algebras$3https://scigraph.springernature.com/ontologies/product-market-codes/M11027 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 615 0$aCommutative algebra. 615 0$aCommutative rings. 615 0$aAlgebraic geometry. 615 0$aAssociative rings. 615 0$aRings (Algebra). 615 0$aPartial differential equations. 615 14$aCommutative Rings and Algebras. 615 24$aAlgebraic Geometry. 615 24$aAssociative Rings and Algebras. 615 24$aPartial Differential Equations. 676 $a512.24 702 $aTu CUONG$b Nguyen$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aTuan HOA$b Le$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aViet TRUNG$b Ngo$4edt$4http://id.loc.gov/vocabulary/relators/edt 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300130403321 996 $aCommutative algebra and its interactions to algebraic geometry$91524244 997 $aUNINA