Titlebook: Six Lectures on Commutative Algebra; J. Elias,J. M. Giral,S. Zarzuela Book 1998 Springer Basel AG 1998 Algebraic geometry.Cohomology theor

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Six Lectures on Commutative Algebra978-3-0346-0329-4Series ISSN 2197-1803 Series E-ISSN 2197-1811

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Modern Birkhäuser Classicshttp://image.papertrans.cn/s/image/868112.jpg

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https://doi.org/10.1007/978-3-0346-0329-4Algebraic geometry; Cohomology theory; Finite; Graded algebra; Graded modules; Hilbert functions; Infinite

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Infinite Free Resolutions,This text is based on the notes for a series of five lectures to the Barcelona . at the Centre de Recerca Matemàtica, Institut d’Estudis Catalans, July 15–26, 1996.

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Tight Closure, Parameter Ideals, and Geometry,These notes are based on five lectures given at the Summer School on Commutative Algebra held at the CRM in Barcelona during July, 1996. I would like to thank the organizers J. Elias, J. M. Giral, R. M. Miró-Roig, and S. Zarzuela for the excellent job they did. The great success of the Summer School was due mainly to their efforts.

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Generic Initial Ideals,s one great insight into the algebra and combinatorics of the ideal. The initial ideal depends on the choice of coordinates, but there is an object, the initial ideal in generic coordinates, which is coordinate-independent. Generic initial ideals appeared in the work of Grauert and Hironaka.

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On the Use of Local Cohomology in Algebra and Geometry,ustrate a few of these techniques. The material presented in the sequel needs some basic knowledge about commutative resp. homological algebra. The basic chapters of the textbooks [9], [28], and [48] are a recommended reading for the preparation. The author’s intention was to present applications of

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Problems and Results on Hilbert Functions of Graded Algebras,be the hypersurfaces containing it. In particular, one would like to know the maximal number of linearly independent hypersurfaces of each degree containing ., that is to know the dimension of .., the vector space of homogeneous polynomials of degree . vanishing on . for various .. Since one knows t