000			02168 a2200277 4500
999			_c51874 _d51874
008			191219b ||||| |||| 00| 0 eng d
020			_a9783319755649
082			_a512.44 CUO
100			_aCuong, Nguyen Tu (ed.)
245			_aCommutative algebra and its interactions to algebraic geometry: VIASM 2013-2014
260			_bSpringer, _c2018 _aCham, Switzerland:
300			_aix; 256p. _bpb; _c24 cm
365			_aEURO _b64.99
440			_aLecture Notes in Mathematics, 0075-8434; Vol.2210
520			_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.
650			_aMathematics.
650			_aRings (Algebra)
650			_aAssociative Rings
650			_aGeometry, Algebraic.
650			_aCommutative Algebra.
650			_aCommutative Rings.
650			_aDifferential equations, Partial.
700			_aHoa, Le Tuan (ed.)
700			_aTrung, Ngo Viet (ed.)
942			_2ddc _cTD