Algebraic Geometry Ii
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Algebraic Geometry Ii Cohomology Of Schemes
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Author : Ulrich Görtz
language : en
Publisher: Springer Nature
Release Date : 2023-11-22
Algebraic Geometry Ii Cohomology Of Schemes written by Ulrich Görtz and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-22 with Mathematics categories.
This book completes the comprehensive introduction to modern algebraic geometry which was started with the introductory volume Algebraic Geometry I: Schemes. It begins by discussing in detail the notions of smooth, unramified and étale morphisms including the étale fundamental group. The main part is dedicated to the cohomology of quasi-coherent sheaves. The treatment is based on the formalism of derived categories which allows an efficient and conceptual treatment of the theory, which is of crucial importance in all areas of algebraic geometry. After the foundations are set up, several more advanced topics are studied, such as numerical intersection theory, an abstract version of the Theorem of Grothendieck-Riemann-Roch, the Theorem on Formal Functions, Grothendieck's algebraization results and a very general version of Grothendieck duality. The book concludes with chapters on curves and on abelian schemes, which serve to develop the basics of the theory of these two important classes of schemes on an advanced level, and at the same time to illustrate the power of the techniques introduced previously. The text contains many exercises that allow the reader to check their comprehension of the text, present further examples or give an outlook on further results.
Algebraic Geometry Ii
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Author : I.R. Shafarevich
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-22
Algebraic Geometry Ii written by I.R. Shafarevich and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-22 with Mathematics categories.
This EMS volume consists of two parts. The first part is devoted to the exposition of the cohomology theory of algebraic varieties. The second part deals with algebraic surfaces. The authors have taken pains to present the material rigorously and coherently. The book contains numerous examples and insights on various topics. This book will be immensely useful to mathematicians and graduate students working in algebraic geometry, arithmetic algebraic geometry, complex analysis and related fields. The authors are well-known experts in the field and I.R. Shafarevich is also known for being the author of volume 11 of the Encyclopaedia.
Lectures On Algebraic Geometry Ii
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Author : Günter Harder
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-04-21
Lectures On Algebraic Geometry Ii written by Günter Harder and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-04-21 with Mathematics categories.
This second volume introduces the concept of shemes, reviews some commutative algebra and introduces projective schemes. The finiteness theorem for coherent sheaves is proved, here again the techniques of homological algebra and sheaf cohomology are needed. In the last two chapters, projective curves over an arbitrary ground field are discussed, the theory of Jacobians is developed, and the existence of the Picard scheme is proved. Finally, the author gives some outlook into further developments- for instance étale cohomology- and states some fundamental theorems.
Algebraic Geometry Ii
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Author : David Mumford
language : en
Publisher:
Release Date : 2015
Algebraic Geometry Ii written by David Mumford and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Algebraic varieties categories.
Several generations of students of algebraic geometry have learned the subject from David Mumford's fabled "Red Book" containing notes of his lectures at Harvard University. This book contains what Mumford had intended to be Volume II. It covers the material in the "Red Book" in more depth with several more topics added.
Homotopical Algebraic Geometry Ii Geometric Stacks And Applications
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Author : Bertrand Toën
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Homotopical Algebraic Geometry Ii Geometric Stacks And Applications written by Bertrand Toën and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
This is the second part of a series of papers called "HAG", devoted to developing the foundations of homotopical algebraic geometry. The authors start by defining and studying generalizations of standard notions of linear algebra in an abstract monoidal model category, such as derivations, étale and smooth morphisms, flat and projective modules, etc. They then use their theory of stacks over model categories to define a general notion of geometric stack over a base symmetric monoidal model category $C$, and prove that this notion satisfies the expected properties.
Integrability Quantization And Geometry Ii Quantum Theories And Algebraic Geometry
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Author : Sergey Novikov
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-04-12
Integrability Quantization And Geometry Ii Quantum Theories And Algebraic Geometry written by Sergey Novikov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-12 with Education categories.
This book is a collection of articles written in memory of Boris Dubrovin (1950–2019). The authors express their admiration for his remarkable personality and for the contributions he made to mathematical physics. For many of the authors, Dubrovin was a friend, colleague, inspiring mentor, and teacher. The contributions to this collection of papers are split into two parts: “Integrable Systems” and “Quantum Theories and Algebraic Geometry”, reflecting the areas of main scientific interests of Dubrovin. Chronologically, these interests may be divided into several parts: integrable systems, integrable systems of hydrodynamic type, WDVV equations (Frobenius manifolds), isomonodromy equations (flat connections), and quantum cohomology. The articles included in the first part are more or less directly devoted to these areas (primarily with the first three listed above). The second part contains articles on quantum theories and algebraic geometry and is less directly connected with Dubrovin's early interests.
Hodge Theory And Complex Algebraic Geometry Ii Volume 2
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Author : Claire Voisin
language : en
Publisher: Cambridge University Press
Release Date : 2003-07-03
Hodge Theory And Complex Algebraic Geometry Ii Volume 2 written by Claire Voisin and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07-03 with Mathematics categories.
The 2003 second volume of this account of Kaehlerian geometry and Hodge theory starts with the topology of families of algebraic varieties. Proofs of the Lefschetz theorem on hyperplane sections, the Picard–Lefschetz study of Lefschetz pencils, and Deligne theorems on the degeneration of the Leray spectral sequence and the global invariant cycles follow. The main results of the second part are the generalized Noether–Lefschetz theorems, the generic triviality of the Abel–Jacobi maps, and most importantly Nori's connectivity theorem, which generalizes the above. The last part of the book is devoted to the relationships between Hodge theory and algebraic cycles. The book concludes with the example of cycles on abelian varieties, where some results of Bloch and Beauville, for example, are expounded. The text is complemented by exercises giving useful results in complex algebraic geometry. It will be welcomed by researchers in both algebraic and differential geometry.
Positivity In Algebraic Geometry Ii
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Author : R.K. Lazarsfeld
language : en
Publisher: Springer
Release Date : 2017-07-25
Positivity In Algebraic Geometry Ii written by R.K. Lazarsfeld and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-25 with Mathematics categories.
This two volume work on "Positivity in Algebraic Geometry" contains a contemporary account of a body of work in complex algebraic geometry loosely centered around the theme of positivity. Topics in Volume I include ample line bundles and linear series on a projective variety, the classical theorems of Lefschetz and Bertini and their modern outgrowths, vanishing theorems, and local positivity. Volume II begins with a survey of positivity for vector bundles, and moves on to a systematic development of the theory of multiplier ideals and their applications. A good deal of this material has not previously appeared in book form, and substantial parts are worked out here in detail for the first time. At least a third of the book is devoted to concrete examples, applications, and pointers to further developments. Whereas Volume I is more elementary, the present Volume II is more at the research level and somewhat more specialized. Both volumes are also available as hardcover editionas Vols. 48 and 49 in the series "Ergebnisse der Mathematik und ihrer Grenzgebiete".
Hodge Theory And Complex Algebraic Geometry
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Author : Claire Voisin
language : en
Publisher:
Release Date : 2003
Hodge Theory And Complex Algebraic Geometry written by Claire Voisin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Geometry, Algebraic categories.
Positivity In Algebraic Geometry 2
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Author : R.K. Lazarsfeld
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-08-24
Positivity In Algebraic Geometry 2 written by R.K. Lazarsfeld and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-08-24 with Mathematics categories.
This two volume work on "Positivity in Algebraic Geometry" contains a contemporary account of a body of work in complex algebraic geometry loosely centered around the theme of positivity. Topics in Volume I include ample line bundles and linear series on a projective variety, the classical theorems of Lefschetz and Bertini and their modern outgrowths, vanishing theorems, and local positivity. Volume II begins with a survey of positivity for vector bundles, and moves on to a systematic development of the theory of multiplier ideals and their applications. A good deal of this material has not previously appeared in book form, and substantial parts are worked out here in detail for the first time. At least a third of the book is devoted to concrete examples, applications, and pointers to further developments. Whereas Volume I is more elementary, the present Volume II is more at the research level and somewhat more specialized. Both volumes are also available as hardcover edition as Vols. 48 and 49 in the series "Ergebnisse der Mathematik und ihrer Grenzgebiete".