The Geometry of Schemes

Author: David Eisenbud,Joe Harris

Publisher: Springer Science & Business Media

ISBN: 0387226397

Category: Mathematics

Page: 300

View: 3014

Grothendieck’s beautiful theory of schemes permeates modern algebraic geometry and underlies its applications to number theory, physics, and applied mathematics. This simple account of that theory emphasizes and explains the universal geometric concepts behind the definitions. In the book, concepts are illustrated with fundamental examples, and explicit calculations show how the constructions of scheme theory are carried out in practice.
Posted in Mathematics

Algebraic Geometry

A Concise Dictionary

Author: Elena Rubei

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3110316234

Category: Mathematics

Page: 239

View: 845

Algebraic geometry has a complicated, difficult language. This book contains a definition, several references and the statements of the main theorems (without proofs) for every of the most common words in this subject. Some terms of related subjects are included. It helps beginners that know some, but not all, basic facts of algebraic geometry to follow seminars and to read papers. The dictionary form makes it easy and quick to consult.
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The Geometry of Syzygies

A Second Course in Algebraic Geometry and Commutative Algebra

Author: David Eisenbud

Publisher: Springer Science & Business Media

ISBN: 0387264566

Category: Mathematics

Page: 246

View: 647

First textbook-level account of basic examples and techniques in this area. Suitable for self-study by a reader who knows a little commutative algebra and algebraic geometry already. David Eisenbud is a well-known mathematician and current president of the American Mathematical Society, as well as a successful Springer author.
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3264 and All That

A Second Course in Algebraic Geometry

Author: David Eisenbud,Joe Harris

Publisher: Cambridge University Press

ISBN: 1107017084

Category: Mathematics

Page: 632

View: 3468

This book can form the basis of a second course in algebraic geometry. As motivation, it takes concrete questions from enumerative geometry and intersection theory, and provides intuition and technique, so that the student develops the ability to solve geometric problems. The authors explain key ideas, including rational equivalence, Chow rings, Schubert calculus and Chern classes, and readers will appreciate the abundant examples, many provided as exercises with solutions available online. Intersection is concerned with the enumeration of solutions of systems of polynomial equations in several variables. It has been an active area of mathematics since the work of Leibniz. Chasles' nineteenth-century calculation that there are 3264 smooth conic plane curves tangent to five given general conics was an important landmark, and was the inspiration behind the title of this book. Such computations were motivation for Poincaré's development of topology, and for many subsequent theories, so that intersection theory is now a central topic of modern mathematics.
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Algebraic Geometry

Author: Robin Hartshorne

Publisher: Springer Science & Business Media

ISBN: 1475738498

Category: Mathematics

Page: 496

View: 7541

An introduction to abstract algebraic geometry, with the only prerequisites being results from commutative algebra, which are stated as needed, and some elementary topology. More than 400 exercises distributed throughout the book offer specific examples as well as more specialised topics not treated in the main text, while three appendices present brief accounts of some areas of current research. This book can thus be used as textbook for an introductory course in algebraic geometry following a basic graduate course in algebra. Robin Hartshorne studied algebraic geometry with Oscar Zariski and David Mumford at Harvard, and with J.-P. Serre and A. Grothendieck in Paris. He is the author of "Residues and Duality", "Foundations of Projective Geometry", "Ample Subvarieties of Algebraic Varieties", and numerous research titles.
Posted in Mathematics

Elementare Algebraische Geometrie

Grundlegende Begriffe und Techniken mit zahlreichen Beispielen und Anwendungen

Author: Klaus Hulek

Publisher: Springer-Verlag

ISBN: 3322802213

Category: Mathematics

Page: 167

View: 2168

Dieses Buch gibt eine Einführung in die Algebraische Geometrie. Ziel ist es, die grundlegenden Begriffe und Techniken der algebraischen Geometrie zusammen mit einer Reihe von Beispielen darzustellen.
Posted in Mathematics

Newsletter

Author: New Zealand Mathematical Society

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 1679

Posted in Mathematics

The Geometry of Moduli Spaces of Sheaves

A Publication of the Max-Planck-Institut für Mathematik, Bonn

Author: Daniel Huybrechts,Manfred Lehn

Publisher: Vieweg+Teubner Verlag

ISBN: 9783663116257

Category: Technology & Engineering

Page: 270

View: 5102

This book is intended to serve as an introduction to the theory of semistable sheaves and at the same time to provide a survey of recent research results on the geometry of moduli spaces. The first part introduces the basic concepts in the theory: Hilbert polynomial, slope, stability, Harder-Narasimhan filtration, Grothendieck's Quot-scheme. It presents detailed proofs of the Grauert-Mülich Theorem, the Bogomolov Inequality, the semistability of tensor products, and the boundedness of the family of semistable sheaves. It also gives a self-contained account of the construction of moduli spaces of semistable sheaves on a projective variety à la Gieseker, Maruyama, and Simpson. The second part presents some of the recent results of the geometry of moduli spaces of sheaves on an algebraic surface, following work of Mukai, O'Grady, Gieseker, Li and many others. In particular, moduli spaces of sheaves on K3 surfaces and determinant line bundles on the moduli spaces are treated in some detail. Other topics include the Serre correspondence, restriction of stable bundles to curves, symplectic structures, irreducibility and Kodaira-dimension of moduli spaces.
Posted in Technology & Engineering

The Geometry of Moduli Spaces of Sheaves

Author: Daniel Huybrechts,Manfred Lehn

Publisher: Cambridge University Press

ISBN: 1139485822

Category: Mathematics

Page: N.A

View: 2580

Now back in print, this highly regarded book has been updated to reflect recent advances in the theory of semistable coherent sheaves and their moduli spaces, which include moduli spaces in positive characteristic, moduli spaces of principal bundles and of complexes, Hilbert schemes of points on surfaces, derived categories of coherent sheaves, and moduli spaces of sheaves on Calabi–Yau threefolds. The authors review changes in the field since the publication of the original edition in 1997 and point the reader towards further literature. References have been brought up to date and errors removed. Developed from the authors' lectures, this book is ideal as a text for graduate students as well as a valuable resource for any mathematician with a background in algebraic geometry who wants to learn more about Grothendieck's approach.
Posted in Mathematics

Vorlesungen über Algebraische Geometrie

Geometrie auf einer Kurve Riemannsche Flächen Abelsche Integrale

Author: Dr. Francesco Severi

Publisher: Springer-Verlag

ISBN: 3663157733

Category: Mathematics

Page: 408

View: 1494

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.
Posted in Mathematics

Jet Schemes and Truncated Wedge Schemes

Author: Cornelia Oichi Yuen

Publisher: N.A

ISBN: N.A

Category:

Page: 92

View: 6241

Our study of jet schemes of determinantal varieties reveals that these schemes are not irreducible in general. We show that the odd jet schemes and the second jet scheme of essentially all determinantal varieties are reducible. In the special case of the variety of matrices of rank at most one, we give the number and dimensions of the irreducible components of its jet schemes.
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Annales de la faculté des sciences de Toulouse

Mathématiques

Author: N.A

Publisher: CNRS

ISBN: 9782271062680

Category: Mathematics

Page: 95

View: 3896

L'effet de serre pose l'un des problèmes majeurs de notre XXe siècle. Les conséquences climatiques commencent à se faire sentir (sécheresses, inondations, extrêmes climatiques comme la vague de chaleur de l'été 2003 en Europe) et inquiètent non seulement les experts du climat mais également la plupart des décideurs politiques, convaincus de la nécessité de prendre des mesures correctives. Mais qu'est-ce que l'effet de serre ? Les prévisions concernant l'évolution du climat sont-elles fiables ? Que nous enseigne l'étude des climats du passé ? D'où proviennent les gaz à effet de serre ? Quelles seront les conséquences du changement climatique dans le monde mais également en France ? Pouvons-nous infléchir la tendance actuelle ? Quelles sont les différentes solutions technologiques et les grands axes de recherche pour lutter contre l'effet de serre ? Quel en sera le coût ? Les gouvernements ont commencé à prendre conscience du problème. Ainsi, en janvier 2000, la France a défini un programme de lutte contre le changement climatique. Qu'en est-il aujourd'hui ? A la suite au Sommet de la Terre de Rio en 1992, les Nations unies ont créé une Convention cadre sur le changement climatique, qui a abouti au fameux Protocole de Kyoto. Après le retrait des Etats-Unis, où en sommes-nous dans l'application de ce protocole ? Les objectifs de limitation des gaz à effet de serre seront-ils atteints ? Autant de questions auxquelles ce livre tente de répondre en considérant la problématique de l'effet de serre dans son ensemble. Il participe ainsi à la nécessaire prise de conscience du rôle des activités humaines sur le climat et ouvre les pistes à explorer pour que l'effet de serre puisse être un jour stabilisé.
Posted in Mathematics

Ebene algebraische Kurven

Author: Gerd Fischer

Publisher: Springer-Verlag

ISBN: 3322803112

Category: Mathematics

Page: 177

View: 8097

Neben den elementaren Dingen, wie Tangenten, Singularitäten und Wendepunkten werden auch schwierigere Begriffe wie lokale Zweige und Geschlecht behandelt. Höhepunkte sind die klassischen Formeln von Plücker und Clebsch, die Beziehungen zwischen verschiedenen globalen und lokalen Invarianten einer Kurve beschreiben.
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Mathematical Reviews

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 2750

Posted in Mathematics

Algebraic Geometry and Arithmetic Curves

Author: Qing Liu,Reinie Erne

Publisher: Oxford University Press

ISBN: 0191547808

Category: Mathematics

Page: 592

View: 5250

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.
Posted in Mathematics