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Varieties in projective space

Shafarevich Basic Algebraic Geometry 2 The second edition of Shafarevich's introduction to algebraic geometry is in two volumes. The second volume covers schemes and complex manifolds, generalisations in two different directions of the affine and projective varieties that form the material of the first volume. Two notable additions in this second edition are the section on moduli spaces and representable functors, motivated by a discussion of the Hilbert scheme, and the section on Khler geometry. The book ends with a historical sketch discussing the origins of algebraic geometry. From the Zentralblatt review of this volume: " ... one can only respectfully repeat what has been said about the first part of the book (...): a great textbook, written by one of the leading algebraic geometers and teachers himself, has been reworked and updated. As a result the author's standard textbook on algebraic geometry has become even more important and valuable. Students, teachers, and active researchers using methods of algebraic and complex-analytic geometry in different areas of mathematics and theoretical physics should be grateful to the author for his renewed service to the mathematical community."

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  • "ji chu dai shu ji he"
  • "Varieties in projective space"
  • "Schemes and complex manifolds"
  • "基础代数几何"
  • "Osnovy algebraicheskoj geometrii"
  • "Osnovy algebraičeskoj geometrii"

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contributor

creator

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  • "Shafarevich Basic Algebraic Geometry 2 The second edition of Shafarevich's introduction to algebraic geometry is in two volumes. The second volume covers schemes and complex manifolds, generalisations in two different directions of the affine and projective varieties that form the material of the first volume. Two notable additions in this second edition are the section on moduli spaces and representable functors, motivated by a discussion of the Hilbert scheme, and the section on Khler geometry. The book ends with a historical sketch discussing the origins of algebraic geometry. From the Zentralblatt review of this volume: " ... one can only respectfully repeat what has been said about the first part of the book (...): a great textbook, written by one of the leading algebraic geometers and teachers himself, has been reworked and updated. As a result the author's standard textbook on algebraic geometry has become even more important and valuable. Students, teachers, and active researchers using methods of algebraic and complex-analytic geometry in different areas of mathematics and theoretical physics should be grateful to the author for his renewed service to the mathematical community.""@en
  • "Shafarevich Basic Algebraic Geometry 2 The second edition of Shafarevich's introduction to algebraic geometry is in two volumes. The second volume covers schemes and complex manifolds, generalisations in two different directions of the affine and projective varieties that form the material of the first volume. Two notable additions in this second edition are the section on moduli spaces and representable functors, motivated by a discussion of the Hilbert scheme, and the section on Kähler geometry. The book ends with a historical sketch discussing the origins of algebraic geometry. From the Zentralblatt review of this volume: "... one can only respectfully repeat what has been said about the first part of the book (...): a great textbook, written by one of the leading algebraic geometers and teachers himself, has been reworked and updated. As a result the author's standard textbook on algebraic geometry has become even more important and valuable. Students, teachers, and active researchers using methods of algebraic and complex-analytic geometry in different areas of mathematics and theoretical physics should be grateful to the author for his renewed service to the mathematical community.""@en
  • "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 in other branches of math who need a liberal education in algebraic geometry, Shafarevich's book is a must.'' The second volume is in two parts: Book II is a gentle cultural introduction to scheme theory, with the first aim of putting abstract algebraic varieties on a firm foundation; a second aim is to introduce Hilbert schemes and moduli spaces, that serve as parameter spaces for other geometric constructions. Book III discusses complex manifolds and their relation with algebraic varieties, Kähler geometry and Hodge theory. The final section raises an important problem in uniformising higher dimensional varieties that has been widely studied as the ̀̀Shafarevich conjecture''. The style of Basic Algebraic Geometry 2 and its minimal prerequisites make it to a large extent independent of Basic Algebraic Geometry 1, and accessible to beginning graduate students in mathematics and in theoretical physics."@en
  • "Algebraic geometry occupied a central place in the mathematics of the last century. The deepest results of Abel, Riemann, Weierstrass, many of the most important papers of Klein and Poincare belong to this do mam. At the end of the last and the beginning of the present century the attitude towards algebraic geometry changed abruptly. Around 1910 Klein wrote: "When I was a student, Abelian functions*-as an after-effect of Jacobi's tradition-were regarded as the undIsputed summit of mathe matics, and each of us, as a matter of course, had the ambition to forge ahead in this field. And now? The young generation hardly know what Abelian functions are." (Vorlesungen tiber die Entwicklung der Mathe matik im XIX. Jahrhundert, Springer-Verlag, Berlin 1926, Seite 312). The style of thinking that was fully developed in algebraic geometry at that time was too far removed from the set-theoretical and axio matic spirit, which then determined the development of mathematics. Several decades had to lapse before the rise of the theory of topolo gical, differentiable and complex manifolds, the general theory of fields, the theory of ideals in sufficiently general rings, and only then it became possible to construct algebraic geometry on the basis of the principles of set-theoretical mathematics. Around the middle of the present century algebraic geometry had undergone to a large extent such a reshaping process. As a result, it can again lay claim to the position it once occupied in mathematics."@en
  • "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 in other branches of math who need a liberal education in algebraic geometry, Shafarevich's book is a must.'' The second volume is in two parts: Book II is a gentle cultural introduction to scheme theory, with the first aim of putting abstract algebraic varieties on a firm foundation; a second aim is to introduce Hilbert schemes and moduli spaces, that serve as parameter spaces for other geometric constructions. Book III discusses complex manifolds and their relation with algebraic varieties, Kähler geometry and Hodge theory. The final section raises an important problem in uniformising higher dimensional varieties that has been widely studied as the ``Shafarevich conjecture''. The style of Basic Algebraic Geometry 2 and its minimal prerequisites make it to a large extent independent of Basic Algebraic Geometry 1, and accessible to beginning graduate students in mathematics and in theoretical physics."

genre

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  • "Electronic books"@en
  • "Lehrbuch"
  • "Textbooks"
  • "Libros electrónicos"

name

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  • "Osnovy algebraičeskoj geometrii"
  • "Basic Algebraic Geometry 1"
  • "[Schemes and complex manifolds]"
  • "Basic algebraic geometry. 1, [Varieties in projective space]"
  • "Basic Algebraic Geometry 2 : Schemes and Complex Manifolds"
  • "Basic algebraic geometry transl. from the russian by K.A.Hirsh"
  • "Основы алгебраической геометрии"
  • "Osnovy algebraicheskoi geometrii"
  • "Basic algebraic geometry / I, Varieties in projective space"
  • "Basic algebraic geometry. 2, [Schemes and complex manifolds]"
  • "Grundzuge der algebraischen geometrie"
  • "Varieties in projective space"
  • "Varieties in projective space"@en
  • "Grundzüge der algebraischen Geometrie"
  • "Osnovy algebraičeskoj geometrii/ 1, Algebraičeskie mnogoobrazija v proektivnom prostranstve"
  • "Basic algebraic geometry / 1 [Varieties in projective space]"
  • "Basic algebraic geometry II. : Schemes and complex manifolds"
  • "Schemes and complex manifolds"
  • "Basic algebraic geometry 2 : schemes and complex manifolds"
  • "Osnovy algebračeskoj geometrii"
  • "Osnovy algebraicheskoĭ geometrii"
  • "Basic algebraic geometry. 2, Schemes and complex manifolds"@en
  • "Basic algebraic geometry. 2, Schemes and complex manifolds"
  • "Basic algebraic geometry 1 : varieties in projective space"
  • "Basic algebraic geometry. 1"
  • "Basic algebraic geometry 1"@en
  • "Basic algebraic geometry. 1, Varieties in projective space"
  • "Basic algebraic geometry"@en
  • "Basic algebraic geometry"
  • "Basic algebraic geometry 2"@en
  • "Basic algebraic geometry. 2"@en
  • "Basic algebraic geometry. 2"
  • "Basic algebraic geometry 1 : [varieties in projective space]"
  • "Basic Algebraic Geometry"
  • "Basic Algebraic Geometry"@en
  • "[Varieties in projective space]"
  • "Basic Algebraic Geometry 2"
  • "Basic Algebraic Geometry 2"@en
  • "Basic Algebraic Geometry 2 Schemes and Complex Manifolds"@en
  • "Basic algebraic geometry / 2, Schemes and complex manifolds"@en
  • "Basic algebraic geometry / 2. [Schemes and complex manifolds]"
  • "Basic Algebraic Geometry 2 Schemes and Complex Manifolds"

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