Geometry of Algebraic Curves: Volume I (Grundlehren der mathematischen Wissenschaften)

In recent years there has been enormous activity in the theory of algebraic curves. Many long-standing problems have been solved using the general techniques developed in algebraic geometry during the 1950's and 1960's. Additionally, unexpected and deep connections between algebraic curves and differential equations have been uncovered, and these in turn shed light on other classical problems in curve theory. It seems fair to say that the theory of algebraic curves looks completely different now from how it appeared 15 years ago; in particular, our current state of knowledge repre sents a significant advance beyond the legacy left by the classical geometers such as Noether, Castelnuovo, Enriques, and Severi. These books give a presentation of one of the central areas of this recent activity; namely, the study of linear series on both a fixed curve (Volume I) and on a variable curve (Volume II). Our goal is to give a comprehensive and self-contained account of the extrinsic geometry of algebraic curves, which in our opinion constitutes the main geometric core of the recent advances in curve theory. Along the way we shall, of course, discuss appli cations of the theory of linear series to a number of classical topics (e.g., the geometry of the Riemann theta divisor) as well as to some of the current research (e.g., the Kodaira dimension of the moduli space of curves).

Geometry of Algebraic Curves: Volume I (Grundlehren der mathematischen Wissenschaften, 267)

Science & Math

Arbarello, Enrico

Cornalba, Maurizio

Griffiths, Phillip

Harris, Joseph Daniel

Mathematics

Springer

A comprehensive, self-contained treatment presenting general results of the theory. Establishes a geometric intuition and a working facility with specific geometric practices. Emphasizes applications through the study of interesting examples and the development of computational tools. Coverage ranges from analytic to geometric. Treats basic techniques and results of complex manifold theory, focusing on results applicable to projective varieties, and includes discussion of the theory of Riemann surfaces and algebraic curves, algebraic surfaces and the quadric line complex as well as special topics in complex manifolds.

Principles of Algebraic Geometry

Harris,Joseph

Wiley-Interscience

Principles of Algebraic Geometry (Pure and Applied Mathematics)

In May, 1979, an NSF Regional Conference was held at the University of Georgia in Athens. The topic of the conference was ``Special divisors on algebraic curves,''. This monograph gives an exposition of the elementary aspects of the theory of special divisors together with an explanation of some more advanced results that are not too technical. As such, it is intended to be an introduction to recent sources. As with most subjects, one may approach the theory of special divisors from several points of view. The one adopted here pertains to Clifford's theorem, and may be informally stated as follows: The failure of a maximally strong version of Clifford's theorem to hold imposes nontrivial conditions on the moduli of an algebraic curve. This monograph contains two sections, respectively studying special divisors using the Riemann-Roch theorem and the Jacobian variety. In the first section the author begins pretty much at ground zero, so that a reader who has only passing familiarity with Riemann surfaces or algebraic curves may be able to follow the discussion. The respective subtopics in this first section are (a) the Riemann-Roch theorem, (b) Clifford's theorem and the $\mu_0$-mapping, and (c) canonical curves and the Brill-Noether matrix. In the second section he assumes a little more, although again an attempt has been made to explain, if not prove, anything. The respective subtopics are (a) Abel's theorem, (b) the reappearance of the Brill-Noether matrix with applications to the singularities of $W_d$ and the Kleiman-Laksov existence proof, (c) special linear systems in low genus.

An Introduction to the Theory of Special Divisors on Algebraic Curves (Cbms Regional Conference Series in Mathematics)

Amer Mathematical Society

Cofiant Y Diweddar Barch: Daniel Griffiths, Soar, Castellnedd. Swydd Forganwg; Yn Cynwys Ei Hanes A'I Nodweddiad Fel Dyn a Gweinidog I Iesu Grist: Yn ... a Marwolaeth Tri O'I Blant (Welsh Edition)

History

Europe

Nabu Press

In recent years there has been enormous activity in the theory of algebraic curves. Many long-standing problems have been solved using the general techniques developed in algebraic geometry during the 1950's and 1960's. Additionally, unexpected and deep connections between algebraic curves and differential equations have been uncovered, and these in turn shed light on other classical problems in curve theory. It seems fair to say that the theory of algebraic curves looks completely different now from how it appeared 15 years ago; in particular, our current state of knowledge repre sents a significant advance beyond the legacy left by the classical geometers such as Noether, Castelnuovo, Enriques, and Severi. These books give a presentation of one of the central areas of this recent activity; namely, the study of linear series on both a fixed curve (Volume I) and on a variable curve (Volume II). Our goal is to give a comprehensive and self-contained account of the extrinsic geometry of algebraic curves, which in our opinion constitutes the main geometric core of the recent advances in curve theory. Along the way we shall, of course, discuss appli cations of the theory of linear series to a number of classical topics (e.g., the geometry of the Riemann theta divisor) as well as to some of the current research (e.g., the Kodaira dimension of the moduli space of curves).

Rational Homotopy Theory and Differential Forms (Progress in Mathematics, 16)

This completely revised and corrected version of the well-known Florence notes circulated by the authors together with E. Friedlander examines basic topology, emphasizing homotopy theory. Included is a discussion of Postnikov towers and rational homotopy theory. This is then followed by an in-depth look at differential forms and de Tham’s theorem on simplicial complexes. In addition, Sullivan’s results on computing the rational homotopy type from forms is presented. 
New to the Second Edition: 
*Fully-revised appendices including an expanded discussion of the Hirsch lemma
*Presentation of a natural proof of a Serre spectral sequence result 
*Updated content throughout the book, reflecting advances in the area of homotopy theory
With its modern approach and timely revisions, this second edition of Rational Homotopy Theory and Differential Forms will be a valuable resource for graduate students and researchers in algebraic topology, differential forms, and homotopy theory.

Morgan, John

Birkhauser

This completely revised and corrected version of the well-known Florence notes circulated by the authors together with E. Friedlander examines basic topology, emphasizing homotopy theory. Included is a discussion of Postnikov towers and rational homotopy theory. This is then followed by an in-depth look at differential forms and de Tham’s theorem on simplicial complexes. In addition, Sullivan’s results on computing the rational homotopy type from forms is presented.  New to the Second Edition: *Fully-revised appendices including an expanded discussion of the Hirsch lemma*Presentation of a natural proof of a Serre spectral sequence result *Updated content throughout the book, reflecting advances in the area of homotopy theoryWith its modern approach and timely revisions, this second edition of Rational Homotopy Theory and Differential Forms will be a valuable resource for graduate students and researchers in algebraic topology, differential forms, and homotopy theory.

The second volume of the Geometry of Algebraic Curves is devoted to the foundations of the theory of moduli of algebraic curves. Its authors are research mathematicians who have actively participated in the development of the Geometry of Algebraic Curves. The subject is an extremely fertile and active one, both within the mathematical community and at the interface with the theoretical physics community. The approach is unique in its blending of algebro-geometric, complex analytic and topological/combinatorial methods. It treats important topics such as Teichmüller theory, the cellular decomposition of moduli and its consequences and the Witten conjecture. The careful and comprehensive presentation of the material is of value to students who wish to learn the subject and to experts as a reference source. 
The first volume appeared 1985 as vol. 267 of the same series.

Geometry of Algebraic Curves: Volume II with a contribution by Joseph Daniel Harris (Grundlehren der mathematischen Wissenschaften, 268)

The second volume of the Geometry of Algebraic Curves is devoted to the foundations of the theory of moduli of algebraic curves. Its authors are research mathematicians who have actively participated in the development of the Geometry of Algebraic Curves. The subject is an extremely fertile and active one, both within the mathematical community and at the interface with the theoretical physics community. The approach is unique in its blending of algebro-geometric, complex analytic and topological/combinatorial methods. It treats important topics such as Teichmüller theory, the cellular decomposition of moduli and its consequences and the Witten conjecture. The careful and comprehensive presentation of the material is of value to students who wish to learn the subject and to experts as a reference source. The first volume appeared 1985 as vol. 267 of the same series.

See the best price to sell, buy, or rent books by Griffiths, Phillip. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Griffiths, Phillip

See the best price to sell, buy, or rent books by Griffiths, Phillip. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Geometry of Algebraic Curves: Volume I (Grundlehren der mathematischen Wissenschaften, 267)

Principles of Algebraic Geometry

Principles of Algebraic Geometry (Pure and Applied Mathematics)

An Introduction to the Theory of Special Divisors on Algebraic Curves (Cbms Regional Conference Series in Mathematics)

Cofiant Y Diweddar Barch: Daniel Griffiths, Soar, Castellnedd. Swydd Forganwg; Yn Cynwys Ei Hanes A'I Nodweddiad Fel Dyn a Gweinidog I Iesu Grist: Yn ... a Marwolaeth Tri O'I Blant (Welsh Edition)

Geometry of Algebraic Curves: Volume I (Grundlehren der mathematischen Wissenschaften)

Rational Homotopy Theory and Differential Forms (Progress in Mathematics, 16)

Rational Homotopy Theory and Differential Forms (Progress in Mathematics, 16)

Geometry of Algebraic Curves: Volume II with a contribution by Joseph Daniel Harris (Grundlehren der mathematischen Wissenschaften, 268)

Geometry of Algebraic Curves: Volume II with a contribution by Joseph Daniel Harris (Grundlehren der mathematischen Wissenschaften, 268)