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Algebraic Geometry


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Realization spaces of polytopes
Realization spaces of polytopes
by Jurgen Richter-gebert
Publisher Comments
The book collects results about realization spaces of polytopes. It gives a presentation of the author's "Universality Theorem for 4-polytopes". It is a comprehensive survey of the important results that have been obtained in that direction. The... (read more)

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London Mathematical Society Lecture Note Series #14: Analytic Theory of Abelian Varieties
London Mathematical Society Lecture Note Series #14: Analytic Theory of Abelian Varieties
by H. P. F. Swinnerton-dyer
Publisher Comments
The study of abelian manifolds forms a natural generalization of the theory of elliptic functions, that is, of doubly periodic functions of one complex variable. When an abelian manifold is embedded in a projective space it is termed an abelian variety... (read more)

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Encyclopaedia of Mathematical Sciences #136: Algebraic Theory of Locally Nilpotent Derivations
Encyclopaedia of Mathematical Sciences #136: Algebraic Theory of Locally Nilpotent Derivations
by Gene Freudenburg
Publisher Comments
This book explores the theory and application of locally nilpotent derivations. It provides a unified treatment of the subject, beginning with sixteen First Principles on which the entire theory is based. These are used to establish classical results... (read more)

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Algebra and Number Theory: Proceedings of a Conference Held at the Institute of Experimental Mathematics, University of Essen (Germany), December
Algebra and Number Theory: Proceedings of a Conference Held at the Institute of Experimental Mathematics, University of Essen (Germany), December
by Gerhard Frey
Book News Annotation
From a December 1992 conference in Essen, Germany, 11 papers discuss such topics as elliptic and algebraic curves, abelian varieties, algebraic surfaces, Galois module structure, and Hilbert's 17th problem (no, not another grandchild). For... (read more)

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Lectures on Algebraic Geometry I: Sheaves, Cohomology of Sheaves, and Applications to Riemann Surfaces (Aspects of Mathematics)
Lectures on Algebraic Geometry I: Sheaves, Cohomology of Sheaves, and Applications to Riemann Surfaces (Aspects of Mathematics)
by Gunter Harder
Publisher Comments
This book and the following second volume is an introduction into modern algebraic geometry. In the first volume the methods of homological algebra, theory of sheaves, and sheaf cohomology are developed. These methods are indispensable for modern... (read more)

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Introduction to Algebraic Geometry and Commutative Algebra
Introduction to Algebraic Geometry and Commutative Algebra
by Dilip P. Patil
Synopsis
This introductory textbook for a graduate course in pure mathematics provides a gateway into the two difficult fields of algebraic geometry and commutative algebra. Algebraic geometry, supported fundamentally by commutative algebra, is a cornerstone of... (read more)

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Algebraic Curves, Algebraic Manifolds and Schemes
Algebraic Curves, Algebraic Manifolds and Schemes
by V. I. Danilov
Publisher Comments
From the reviews: "This volume... consists of two papers. The first, written by V.V. Shokurov, is devoted to the theory of Riemann surfaces and algebraic curves. It is an excellent overview of the theory of relations between Riemann surfaces and their... (read more)

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Methods of Algebraic Geometry (Cambridge Mathematical Library)
Methods of Algebraic Geometry (Cambridge Mathematical Library)
by W. V. D. Hodge
Publisher Comments
This classic work (first published in 1947), in three volumes, provides a lucid and rigorous account of the foundations of modern algebraic geometry. The authors have confined themselves to fundamental concepts and geometrical methods, and do not give... (read more)

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Invariant Methods in Discrete and Computational Geometry
Invariant Methods in Discrete and Computational Geometry
by Neil L. White
Publisher Comments
Invariant, or coordinate-free methods provide a natural framework for many geometric questions. Invariant Methods in Discrete and Computational Geometry provides a basic introduction to several aspects of invariant theory, including the supersymmetric... (read more)

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Complex Algebraic Varieties
Complex Algebraic Varieties
by Klaus Hulek
Publisher Comments
The Bayreuth meeting on "Complex Algebraic Varieties" focussed on the classification of algebraic varieties and topics such as vector bundles, Hodge theory and hermitian differential geometry. Most of the articles in this volume are closely related to... (read more)

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Complex Functions: An Algebraic and Geometric Viewpoint
Complex Functions: An Algebraic and Geometric Viewpoint
by Gareth A. Jones
Publisher Comments
Elliptic functions and Riemann surfaces played an important role in nineteenth-century mathematics. At the present time there is a great revival of interest in these topics not only for their own sake but also because of their applications to so many... (read more)

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Approximate Commutative Algebra (Texts and Monographs in Symbolic Computation)
Approximate Commutative Algebra (Texts and Monographs in Symbolic Computation)
by Lorenzo (edt) Robbiano
Publisher Comments
Approximate Commutative Algebra is an emerging field of research which endeavours to bridge the gap between traditional exact Computational Commutative Algebra and approximate numerical computation. The last 50 years have seen enormous progress in the... (read more)

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Ergebnisse Der Mathematik Und Ihrer Grenzgebiete. 3. Folge a #52: Mixed Hodge Structures
Ergebnisse Der Mathematik Und Ihrer Grenzgebiete. 3. Folge a #52: Mixed Hodge Structures
by Chris A. M. Peters
Publisher Comments
This is comprehensive basic monograph on mixed Hodge structures. Building up from basic Hodge theory the book explains Delingne's mixed Hodge theory in a detailed fashion. Then both Hain's and Morgan's approaches to mixed Hodge theory related to homotopy... (read more)

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Lecture Notes in Mathematics #1314: Kahler-Einstein Metrics and Integral Invariants
Lecture Notes in Mathematics #1314: Kahler-Einstein Metrics and Integral Invariants
by Akito Futaki
Publisher Comments
These notes present very recent results on compact Kähler-Einstein manifolds of positive scalar curvature. A central role is played here by a Lie algebra character of the complex Lie algebra consisting of all holomorphic vector fields, which can be... (read more)

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Moufang Polygons
Moufang Polygons
by Jacques Tits
Publisher Comments
This book gives the complete classification of Moufang polygons, starting from first principles. In particular, it may serve as an introduction to the various important algebraic concepts which arise in this classification including alternative division... (read more)

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Tropical Geometry & Integrable Sysems
Tropical Geometry & Integrable Sysems
by Chris Athorne
Publisher Comments
Two of the nine papers in this collection introduce tropical geometry and integrable systems to specialists in the other, emphasizing the max-plus algebra and other features common to both areas of mathematics. Other topics include counting algebraic... (read more)

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The Grothendieck Festschrift Volume I: A Collection of Articles Written in Honor of the 60th Birthday of Alexander Grothendieck (Modern Birkhuser Classics)
The Grothendieck Festschrift Volume I: A Collection of Articles Written in Honor of the 60th Birthday of Alexander Grothendieck (Modern Birkhuser Classics)
by Pierre Cartier
Publisher Comments
This three-volume work contains articles collected on the occasion of Alexander Grothendieck's sixtieth birthday and originally published in 1990. The articles were offered as a tribute to one of the world's greatest living mathematicians. Many of the... (read more)

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Moduli of Abelian Varieties, Vol. VI
Moduli of Abelian Varieties, Vol. VI
by Allan Adler
Publisher Comments
This is a book aimed at researchers and advanced graduate students in algebraic geometry, interested in learning about a promising direction of research in algebraic geometry. It begins with a generalization of parts of Mumford's theory of the equations... (read more)

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Spectra of Graphs (Universitext)
Spectra of Graphs (Universitext)
by Andries E. Brouwer
Publisher Comments
This book provides an elementary treatment of the basic material about graph spectra, both for ordinary, and Laplace and Seidel spectra. It covers standard topics such as bounds on the sizes of cliques and cocliques, chromatic number and Shannon capacity,... (read more)

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Positivity in Algebraic Geometry I: Classical Setting: Line Bundles and Linear Series
Positivity in Algebraic Geometry I: Classical Setting: Line Bundles and Linear Series
by Robert Lazarsfeld
Publisher Comments
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... (read more)

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