An Arithmetic Riemann Roch Theorem For Singular Arithmetic Surfaces
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An Arithmetic Riemann Roch Theorem For Singular Arithmetic Surfaces
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Author : Wayne Aitken
language : en
Publisher: American Mathematical Soc.
Release Date : 1996
An Arithmetic Riemann Roch Theorem For Singular Arithmetic Surfaces written by Wayne Aitken 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 1996 with Mathematics categories.
The following gives a development of Arakelov theory general enough to handle not only regular arithmetic surfaces but also a large class of arithmetic surfaces whose generic fiber has singularities. This development culminates in an arithmetic Riemann-Roch theorem for such arithmetic surfaces. The first part of the memoir gives a treatment of Deligne's functorial intersection theory, and the second develops a class of intersection functions for singular curves which behaves analogously to the canonical Green's functions introduced by Arakelov for smooth curves.
Lectures On The Arithmetic Riemann Roch Theorem
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Author : Gerd Faltings
language : en
Publisher: Princeton University Press
Release Date : 1992-03-10
Lectures On The Arithmetic Riemann Roch Theorem written by Gerd Faltings and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-03-10 with Mathematics categories.
The arithmetic Riemann-Roch Theorem has been shown recently by Bismut-Gillet-Soul. The proof mixes algebra, arithmetic, and analysis. The purpose of this book is to give a concise introduction to the necessary techniques, and to present a simplified and extended version of the proof. It should enable mathematicians with a background in arithmetic algebraic geometry to understand some basic techniques in the rapidly evolving field of Arakelov-theory.
Lectures On The Arithmetic Riemann Roch Theorem
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Author : Gerd Faltings
language : en
Publisher:
Release Date : 1992
Lectures On The Arithmetic Riemann Roch Theorem written by Gerd Faltings and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Geometry, Algebraic categories.
The arithmetic Riemann-Roch Theorem has been shown recently by Bismut-Gillet-Soul. The proof mixes algebra, arithmetic, and analysis. The purpose of this book is to give a concise introduction to the necessary techniques, and to present a simplified and extended version of the proof. It should enable mathematicians with a background in arithmetic algebraic geometry to understand some basic techniques in the rapidly evolving field of Arakelov-theory.
Algebraic Surfaces
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Author : G. Tomassini
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-06
Algebraic Surfaces written by G. Tomassini 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 2011-06-06 with Mathematics categories.
Lectures: A. Beauville: Surfaces algébriques complexes.- F.A. Bogomolov: The theory of invariants and its applications to some problems in the algebraic geometry.- E. Bombieri: Methods of algebraic geometry in Char. P and their applications.- Seminars: F. Catanese: Pluricanonical mappings of surfaces with K2 =1,2, q=pg=0.- F. Catanese: On a class of surfaces of general type.- I. Dolgacev: Algebraic surfaces with p=pg =0.- A. Tognoli: Some remarks about the "Nullstellensatz".
An Introduction To The Theory Of Algebraic Surfaces
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Author : Oscar Zariski
language : en
Publisher: Springer
Release Date : 2006-11-14
An Introduction To The Theory Of Algebraic Surfaces written by Oscar Zariski and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Riemann Roch Spaces And Computation
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Author : Paraskevas Alvanos
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2015-03-11
Riemann Roch Spaces And Computation written by Paraskevas Alvanos and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-11 with Computers categories.
The book focuses on the educational perspective of Riemann-Roch spaces and the computation of algebraic structures connected to the Riemann-Roch theorem, which is a useful tool in fields of complex analysis and algebraic geometry. On one hand, the theorem connects the Riemann surface with its topological genus, and on the other it allows us to compute the algebraic function field spaces. In the first part of this book, algebraic structures and some of their properties are presented. The second part shows efficient algorithms and examples connected to Riemann-Roch spaces. What is important, a variety of examples with codes of algorithms are given in the book, covering the majority of the cases.
Theory Of Algebraic Surfaces
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Author : Kunihiko Kodaira
language : en
Publisher: Springer Nature
Release Date : 2020-09-17
Theory Of Algebraic Surfaces written by Kunihiko Kodaira and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-17 with Mathematics categories.
This is an English translation of the book in Japanese, published as the volume 20 in the series of Seminar Notes from The University of Tokyo that grew out of a course of lectures by Professor Kunihiko Kodaira in 1967. It serves as an almost self-contained introduction to the theory of complex algebraic surfaces, including concise proofs of Gorenstein's theorem for curves on a surface and Noether's formula for the arithmetic genus. It also discusses the behavior of the pluri-canonical maps of surfaces of general type as a practical application of the general theory. The book is aimed at graduate students and also at anyone interested in algebraic surfaces, and readers are expected to have only a basic knowledge of complex manifolds as a prerequisite.
Algebraic Geometry And Arithmetic Curves
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Author : Qing Liu
language : en
Publisher: Oxford University Press
Release Date : 2006-06-29
Algebraic Geometry And Arithmetic Curves written by Qing Liu and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-29 with Mathematics categories.
This book is a general introduction to the theory of schemes, followed by applications to arithmetic surfaces and to the theory of reduction of algebraic curves. The first part introduces basic objects such as schemes, morphisms, base change, local properties (normality, regularity, Zariski's Main Theorem). This is followed by the more global aspect: coherent sheaves and a finiteness theorem for their cohomology groups. Then follows a chapter on sheaves of differentials, dualizing sheaves, and Grothendieck's duality theory. The first part ends with the theorem of Riemann-Roch and its application to the study of smooth projective curves over a field. Singular curves are treated through a detailed study of the Picard group. The second part starts with blowing-ups and desingularisation (embedded or not) of fibered surfaces over a Dedekind ring that leads on to intersection theory on arithmetic surfaces. Castelnuovo's criterion is proved and also the existence of the minimal regular model. This leads to the study of reduction of algebraic curves. The case of elliptic curves is studied in detail. The book concludes with the funadmental theorem of stable reduction of Deligne-Mumford. The book is essentially self-contained, including the necessary material on commutative algebra. The prerequisites are therefore few, and the book should suit a graduate student. It contains many examples and nearly 600 exercises.
Topics In The Theory Of Riemann Surfaces
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Author : Robert D.M. Accola
language : en
Publisher: Springer
Release Date : 2006-11-14
Topics In The Theory Of Riemann Surfaces written by Robert D.M. Accola and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
The book's main concern is automorphisms of Riemann surfaces, giving a foundational treatment from the point of view of Galois coverings, and treating the problem of the largest automorphism group for a Riemann surface of a given genus. In addition, the extent to which fixed points of automorphisms are generalized Weierstrass points is considered. The extremely useful inequality of Castelnuovo- Severi is also treated. While the methods are elementary, much of the material does not appear in the current texts on Riemann surfaces, algebraic curves. The book is accessible to a reader who has had an introductory course on the theory of Riemann surfaces or algebraic curves.
The Riemann Boundary Problem On Riemann Surfaces
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Author : Y. Rodin
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
The Riemann Boundary Problem On Riemann Surfaces written by Y. Rodin 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 2013-06-29 with Mathematics categories.
Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van GuIik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.