- Filename: algebraic-geometry-and-commutative-algebra.
- ISBN: 9781447148296
- Release Date: 2012-11-15
- Number of pages: 504
- Author: Siegfried Bosch
- Publisher: Springer Science & Business Media

Algebraic geometry is a fascinating branch of mathematics that combines methods from both, algebra and geometry. It transcends the limited scope of pure algebra by means of geometric construction principles. Moreover, Grothendieck’s schemes invented in the late 1950s allowed the application of algebraic-geometric methods in fields that formerly seemed to be far away from geometry, like algebraic number theory. The new techniques paved the way to spectacular progress such as the proof of Fermat’s Last Theorem by Wiles and Taylor. The scheme-theoretic approach to algebraic geometry is explained for non-experts. More advanced readers can use the book to broaden their view on the subject. A separate part deals with the necessary prerequisites from commutative algebra. On a whole, the book provides a very accessible and self-contained introduction to algebraic geometry, up to a quite advanced level. Every chapter of the book is preceded by a motivating introduction with an informal discussion of the contents. Typical examples and an abundance of exercises illustrate each section. This way the book is an excellent solution for learning by yourself or for complementing knowledge that is already present. It can equally be used as a convenient source for courses and seminars or as supplemental literature.

- Filename: an-invitation-to-algebraic-geometry.
- ISBN: 0387989803
- Release Date: 2000-10-31
- Number of pages: 155
- Author: Karen E. Smith
- Publisher: Springer Science & Business Media

The underlying principles of algebraic geometry, 20th-century developments, and the challenges facing practitioners today are discussed in this book, intended for the working or the aspiring mathematician who is unfamiliar with algebraic geometry.

- Filename: algebraic-geometry-over-the-complex-numbers.
- ISBN: 9781461418092
- Release Date: 2012-02-15
- Number of pages: 329
- Author: Donu Arapura
- Publisher: Springer Science & Business Media

This is a relatively fast paced graduate level introduction to complex algebraic geometry, from the basics to the frontier of the subject. It covers sheaf theory, cohomology, some Hodge theory, as well as some of the more algebraic aspects of algebraic geometry. The author frequently refers the reader if the treatment of a certain topic is readily available elsewhere but goes into considerable detail on topics for which his treatment puts a twist or a more transparent viewpoint. His cases of exploration and are chosen very carefully and deliberately. The textbook achieves its purpose of taking new students of complex algebraic geometry through this a deep yet broad introduction to a vast subject, eventually bringing them to the forefront of the topic via a non-intimidating style.

- Filename: algebraic-geometry.
- ISBN: 1848000561
- Release Date: 2007-12-16
- Number of pages: 263
- Author: Daniel Perrin
- Publisher: Springer Science & Business Media

Aimed primarily at graduate students and beginning researchers, this book provides an introduction to algebraic geometry that is particularly suitable for those with no previous contact with the subject; it assumes only the standard background of undergraduate algebra. The book starts with easily-formulated problems with non-trivial solutions and uses these problems to introduce the fundamental tools of modern algebraic geometry: dimension; singularities; sheaves; varieties; and cohomology. A range of exercises is provided for each topic discussed, and a selection of problems and exam papers are collected in an appendix to provide material for further study.

- Filename: algebraic-geometry.
- ISBN: 9780821893968
- Release Date: 2013-02-01
- Number of pages: 335
- Author: Thomas A. Garrity
- Publisher: American Mathematical Soc.

Algebraic Geometry has been at the center of much of mathematics for hundreds of years. It is not an easy field to break into, despite its humble beginnings in the study of circles, ellipses, hyperbolas, and parabolas. This text consists of a series of ex

- Filename: complex-geometry.
- ISBN: 3540212906
- Release Date: 2005
- Number of pages: 309
- Author: Daniel Huybrechts
- Publisher: Springer Science & Business Media

This accessible introduction to the contemporary theory of compact complex manifolds emphasizes Kahler manifolds in their various aspects and applications. It contains accounts of basic concepts, exercises to illustrate the theory, and chapter appendices that cover recent research. Two appendices at the end of the book recall basic facts from differential geometry, Hodge theory on differential manifold, sheaf theory and sheaf cohomology.

- Filename: algebraic-geometry-and-commutative-algebra.
- ISBN: 9781447148296
- Release Date: 2012-11-15
- Number of pages: 504
- Author: Siegfried Bosch
- Publisher: Springer Science & Business Media

Algebraic geometry is a fascinating branch of mathematics that combines methods from both, algebra and geometry. It transcends the limited scope of pure algebra by means of geometric construction principles. Moreover, Grothendieck’s schemes invented in the late 1950s allowed the application of algebraic-geometric methods in fields that formerly seemed to be far away from geometry, like algebraic number theory. The new techniques paved the way to spectacular progress such as the proof of Fermat’s Last Theorem by Wiles and Taylor. The scheme-theoretic approach to algebraic geometry is explained for non-experts. More advanced readers can use the book to broaden their view on the subject. A separate part deals with the necessary prerequisites from commutative algebra. On a whole, the book provides a very accessible and self-contained introduction to algebraic geometry, up to a quite advanced level. Every chapter of the book is preceded by a motivating introduction with an informal discussion of the contents. Typical examples and an abundance of exercises illustrate each section. This way the book is an excellent solution for learning by yourself or for complementing knowledge that is already present. It can equally be used as a convenient source for courses and seminars or as supplemental literature.

- Filename: higher-dimensional-algebraic-geometry.
- ISBN: 0387952276
- Release Date: 2001-06-26
- Number of pages: 234
- Author: Olivier Debarre
- Publisher: Springer Science & Business Media

The classification theory of algebraic varieties is the focus of this book. This very active area of research is still developing, but an amazing quantity of knowledge has accumulated over the past twenty years. The authors goal is to provide an easily accessible introduction to the subject. The book starts with preparatory and standard definitions and results, then moves on to discuss various aspects of the geometry of smooth projective varieties with many rational curves, and finishes in taking the first steps towards Moris minimal model program of classification of algebraic varieties by proving the cone and contraction theorems. The book is well-organized and the author has kept the number of concepts that are used but not proved to a minimum to provide a mostly self-contained introduction.

- Filename: algebraic-surfaces-and-holomorphic-vector-bundles.
- ISBN: 0387983619
- Release Date: 1998-01-23
- Number of pages: 328
- Author: Robert Friedman
- Publisher: Springer Science & Business Media

The goal of this book is to provide a unified introduction to the study of algebraic surfaces and of holomorphic vector bundles on them. The author keeps the prerequisites to a good working knowledge of Hartshorne's book on algebraic geometry. The book will appeal to graduate students and researchers in the areas of algebraic geometry, gauge thoery, or 4-manifold topolgogy, as well as to physicists studying string theory.

- Filename: snowbird-lectures-in-algebraic-geometry.
- ISBN: 9780821837191
- Release Date: 2005
- Number of pages: 188
- Author: Ravi Vakil
- Publisher: American Mathematical Soc.

A significant part of the 2004 Summer Research Conference on Algebraic Geometry (Snowbird, UT) was devoted to lectures introducing the participants, in particular, graduate students and recent Ph.D.'s, to a wide swathe of algebraic geometry and giving them a working familiarity with exciting, rapidly developing parts of the field. One of the main goals of the organizers was to allow the participants to broaden their horizons beyond the narrow area in which they are working. A fine selection of topics and a noteworthy list of contributors made the resulting collection of articles a useful resource for everyone interested in getting acquainted with the modern topic of algebraic geometry.The book consists of ten articles covering, among others, the following topics: the minimal model program, derived categories of sheaves on algebraic varieties, Kobayashi hyperbolicity, groupoids and quotients in algebraic geometry, rigid analytic varieties, and equivariant cohomology. Suitable for independent study, this unique volume is intended for graduate students and researchers interested in algebraic geometry.

- Filename: combinatorial-algebraic-geometry.
- ISBN: 9783319048703
- Release Date: 2014-05-15
- Number of pages: 239
- Author: Aldo Conca
- Publisher: Springer

Combinatorics and Algebraic Geometry have enjoyed a fruitful interplay since the nineteenth century. Classical interactions include invariant theory, theta functions and enumerative geometry. The aim of this volume is to introduce recent developments in combinatorial algebraic geometry and to approach algebraic geometry with a view towards applications, such as tensor calculus and algebraic statistics. A common theme is the study of algebraic varieties endowed with a rich combinatorial structure. Relevant techniques include polyhedral geometry, free resolutions, multilinear algebra, projective duality and compactifications.

- Filename: contributions-to-algebraic-geometry.
- ISBN: 3037191147
- Release Date: 2012
- Number of pages: 504
- Author: Piotr Pragacz
- Publisher: European Mathematical Society

The articles in this volume cover a broad range of topics in algebraic geometry: classical varieties, linear system, birational geometry, Minimal Model Program, moduli spaces, toric varieties, enumerative theory of singularities, equivariant cohomology and arithmetic questions.

- Filename: advances-in-algebraic-geometry-codes.
- ISBN: 9789812794017
- Release Date: 2008
- Number of pages: 452
- Author: Edgar Martinez-Moro
- Publisher: World Scientific

Advances in Algebraic Geometry Codes presents the most successful applications of algebraic geometry to the field of error-correcting codes, which are used in the industry when one sends information through a noisy channel. The noise in a channel is the corruption of a part of the information due to either interferences in the telecommunications or degradation of the information-storing support (for instance, compact disc). An error-correcting code thus adds extra information to the message to be transmitted with the aim of recovering the sent information. With contributions from renowned researchers, this pioneering book will be of value to mathematicians, computer scientists, and engineers in information theory.

- Filename: interactions-of-classical-and-numerical-algebraic-geometry.
- ISBN: 9780821847466
- Release Date: 2009-09-16
- Number of pages: 362
- Author: Daniel James Bates
- Publisher: American Mathematical Soc.

This volume contains the proceedings of the conference on Interactions of Classical and Numerical Algebraic Geometry, held May 22-24, 2008, at the University of Notre Dame, in honor of the achievements of Professor Andrew J. Sommese. While classical algebraic geometry has been studied for hundreds of years, numerical algebraic geometry has only recently been developed. Due in large part to the work of Andrew Sommese and his collaborators, the intersection of these two fields is now ripe for rapid advancement. The primary goal of both the conference and this volume is to foster the interaction between researchers interested in classical algebraic geometry and those interested in numerical methods. The topics in this book include (but are not limited to) various new results in complex algebraic geometry, a primer on Seshadri constants, analyses and presentations of existing and novel numerical homotopy methods for solving polynomial systems, a numerical method for computing the dimensions of the cohomology of twists of ideal sheaves, and the application of algebraic methods in kinematics and phylogenetics.

- Filename: classical-algebraic-geometry.
- ISBN: 9781107017658
- Release Date: 2012-08-16
- Number of pages: 639
- Author: Igor V. Dolgachev
- Publisher: Cambridge University Press

Makes classical algebraic geometry accessible to the modern mathematician.