Titlebook: Basic Algebraic Geometry 1; Varieties in Project Igor R. Shafarevich Textbook 2013Latest edition Springer-Verlag Berlin Heidelberg 2013 alg

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Quellen- und Literaturverzeichnis (Auswahl),nate ring and the latter the field of rational functions. The notions of products of varieties and their dimension are discussed. In addition to definitions and their basic corollaries, proofs of several nontrivial results are given, including properness and dimensions of intersections.

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,Aus der Arbeit der Universit?tsinstitute,ar or algebraic equivalence. A first aim is a rigorous treatment of Bézout’s theorem for the intersection of two curves in the plane. Algebraic cycle class groups and their intersection theory play a role analogous to homology and cohomology in the topology of manifolds. A number of topics are discu

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Textbook 2013Latest editionago. As the translator writes in a prefatory note, ``For all [advanced undergraduate and beginning graduate] students, and for the many specialists in other branches of math who need a liberal education in algebraic geometry, Shafarevich’s book is a must.‘‘ The third edition, in addition to some min

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Quellen- und Literaturverzeichnis (Auswahl), the algebraic idea that the affine coordinate rings are integrally closed. This implies that the singular locus has codimension at least 2, so that every codimension 1 subvariety defines a valuation of the field of fractions. Finally, the notion of singularity and ramification are extended to regular maps between varieties.

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,Aus der Arbeit der Universit?tsinstitute,ssed as applications of these ideas, including the adjunction formula for the genus of a curve on a surface, the factorisation of a rational map between nonsingular surfaces into blowups and blowdowns and the classification of Du Val singularities.

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l: .Shafarevich‘s Basic Algebraic Geometry has been a classic and universally used introduction? to the subject since its first appearance over 40 years ago. As the translator writes in a prefatory note, ``For all [advanced undergraduate and beginning graduate] students, and for the many specialists

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