Mathematics

Algebraic Geometry

Author: Robin Hartshorne

Publisher: Springer Science & Business Media

ISBN:

Category: Mathematics

Page: 496

View: 393

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.
Mathematics

Algebraic Geometry

Author: Daniel Bump

Publisher: World Scientific

ISBN:

Category: Mathematics

Page: 218

View: 186

This is a graduate-level text on algebraic geometry that provides a quick and fully self-contained development of the fundamentals, including all commutative algebra which is used. A taste of the deeper theory is given: some topics, such as local algebra and ramification theory, are treated in depth. The book culminates with a selection of topics from the theory of algebraic curves, including the Riemann-Roch theorem, elliptic curves, the zeta function of a curve over a finite field, and the Riemann hypothesis for elliptic curves.
Mathematics

Vector Bundles in Algebraic Geometry

Author: N. J. Hitchin

Publisher: Cambridge University Press

ISBN:

Category: Mathematics

Page: 345

View: 372

The study of vector bundles over algebraic varieties has been stimulated over the last few years by successive waves of migrant concepts, largely from mathematical physics, whilst retaining its roots in old questions concerning subvarieties of projective space. The 1993 Durham Symposium on Vector Bundles in Algebraic Geometry brought together some of the leading researchers in the field to explore further these interactions. This book is a collection of survey articles by the main speakers at the symposium and presents to the mathematical world an overview of the key areas of research involving vector bundles. Topics covered include those linking gauge theory and geometric invariant theory such as augmented bundles and coherent systems; Donaldson invariants of algebraic surfaces; Floer homology and quantum cohomology; conformal field theory and the moduli spaces of bundles on curves; the Horrocks–Mumford bundle and codimension 2 subvarieties in P4 and P5; exceptional bundles and stable sheaves on projective space.
Mathematics

Algebraic Geometry I

Author: V.I. Danilov

Publisher: Springer Science & Business Media

ISBN:

Category: Mathematics

Page: 310

View: 985

"... To sum up, this book helps to learn algebraic geometry in a short time, its concrete style is enjoyable for students and reveals the beauty of mathematics." --Acta Scientiarum Mathematicarum
Mathematics

New Trends in Algebraic Geometry

Author: K. Hulek

Publisher: Cambridge University Press

ISBN:

Category: Mathematics

Page: 484

View: 495

Seventeen articles from the most outstanding contemporary topics in algebraic geometry.
Mathematics

Algebraic Geometry I

Author: David Mumford

Publisher: Springer Science & Business Media

ISBN:

Category: Mathematics

Page: 186

View: 726

From the reviews: "Although several textbooks on modern algebraic geometry have been published in the meantime, Mumford's "Volume I" is, together with its predecessor the red book of varieties and schemes, now as before one of the most excellent and profound primers of modern algebraic geometry. Both books are just true classics!" Zentralblatt
Mathematics

Algebraic Geometry: Sheaves and cohomology

Author: 健爾·上野

Publisher: American Mathematical Soc.

ISBN:

Category: Mathematics

Page: 184

View: 222

Modern algebraic geometry is built upon two fundamental notions: schemes and sheaves. The theory of schemes is presented in the first part of this book (Algebraic Geometry 1: From Algebraic Varieties to Schemes, AMS, 1999, Translations of Mathematical Monographs, Volume 185). In the present book, the author turns to the theory of sheaves and their cohomology. Loosely speaking, a sheaf is a way of keeping track of local information defined on a topological space, such as the local algebraic functions on an algebraic manifold or the local sections of a vector bundle. Sheaf cohomology is a primary tool in understanding sheaves and using them to study properties of the corresponding manifolds. The text covers the important topics of the theory of sheaves on algebraic varieties, including types of sheaves and the fundamental operations on them, such as coherent and quasicoherent sheaves, direct and inverse images, behavior of sheaves under proper and projective morphisms, and Cech cohomology. The book contains numerous problems and exercises with solutions. It would be an excellent text for the second part of a course in algebraic geometry.
Mathematics

Algebraic Geometry: From algebraic varieties to schemes

Author: Kenji Ueno

Publisher: American Mathematical Soc.

ISBN:

Category: Mathematics

Page: 154

View: 855

Beginning algebraic geometers are well served by Uneno's inviting introduction to the language of schemes. Grothendieck's schemes and Zariski's emphasis on algebra and rigor are primary sources for this introduction to a rich mathematical subject. Ueno's book is a self-contained text suitable for an introductory course on algebraic geometry.
Mathematics

Algebraic Geometry

Author: Spencer Bloch

Publisher: American Mathematical Soc.

ISBN:

Category: Mathematics

Page: 481

View: 475

Mathematics

Rudiments of Algebraic Geometry

Author: W.E. Jenner

Publisher: Courier Dover Publications

ISBN:

Category: Mathematics

Page: 112

View: 660

Aimed at advanced undergraduate students of mathematics, this concise text covers the basics of algebraic geometry. Topics include affine spaces, projective spaces, rational curves, algebraic sets with group structure, more. 1963 edition.