Model Theory and Algebraic Geometry

Model Theory and Algebraic Geometry

An Introduction to E. Hrushovski's Proof of the Geometric Mordell-Lang Conjecture Elisabeth Bouscaren ... In order to understand one needs a minimal knowledge of the basics of algebraic geometry but, more importantly, a good knowledge ...

Author: Elisabeth Bouscaren

Publisher: Springer Science & Business Media

ISBN: 9783540648635

Category: Mathematics

Page: 211

View: 988

This introduction to the recent exciting developments in the applications of model theory to algebraic geometry, illustrated by E. Hrushovski's model-theoretic proof of the geometric Mordell-Lang Conjecture starts from very basic background and works up to the detailed exposition of Hrushovski's proof, explaining the necessary tools and results from stability theory on the way. The first chapter is an informal introduction to model theory itself, making the book accessible (with a little effort) to readers with no previous knowledge of model theory. The authors have collaborated closely to achieve a coherent and self- contained presentation, whereby the completeness of exposition of the chapters varies according to the existence of other good references, but comments and examples are always provided to give the reader some intuitive understanding of the subject.
Categories: Mathematics

Methods of Algebraic Geometry in Control Theory Part II

Methods of Algebraic Geometry in Control Theory  Part II

Peter Falb Methods of Algebraic Geometry in Control Theory Part II - Multivariable Linear Systems and Projective Algebraic Geometry "An introduction to the ideas of algebraic geometry in the motivated context of system theory.

Author: Peter Falb

Publisher: Birkhäuser

ISBN: 0817641130

Category: Mathematics

Page: 390

View: 391

"Control theory represents an attempt to codify, in mathematical terms, the principles and techniques used in the analysis and design of control systems. Algebraic geometry may, in an elementary way, be viewed as the study of the structure and properties of the solutions of systems of algebraic equations. The aim of this book is to provide access to the methods of algebraic geometry for engineers and applied scientists through the motivated context of control theory" .* The development which culminated with this volume began over twenty-five years ago with a series of lectures at the control group of the Lund Institute of Technology in Sweden. I have sought throughout to strive for clarity, often using constructive methods and giving several proofs of a particular result as well as many examples. The first volume dealt with the simplest control systems (i.e., single input, single output linear time-invariant systems) and with the simplest algebraic geometry (i.e., affine algebraic geometry). While this is quite satisfactory and natural for scalar systems, the study of multi-input, multi-output linear time invariant control systems requires projective algebraic geometry. Thus, this second volume deals with multi-variable linear systems and pro jective algebraic geometry. The results are deeper and less transparent, but are also quite essential to an understanding of linear control theory. A review of * From the Preface to Part 1. viii Preface the scalar theory is included along with a brief summary of affine algebraic geometry (Appendix E).
Categories: Mathematics

Methods of Algebraic Geometry

Methods of Algebraic Geometry

Methods of Algebraic Geometry Volume 2 W. V. D. HODGE & D. PEDOE This work provides a lucid and rigorous account of the foundations and methods of modern algebraic geometry . The authors have confined themselves to fundamental concepts ...

Author: William Vallance Douglas Hodge

Publisher: CUP Archive

ISBN:

Category: Geometry, Algebraic

Page: 440

View: 411

This classic work, 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 detailed developments of geometrical properties but geometrical meaning has been emphasized throughout.
Categories: Geometry, Algebraic

Algebraic Geometry IV

Algebraic Geometry IV

Linear Algebraic Groups Invariant Theory A.N. Parshin, I.R. Shafarevich. is open , affine , and invariant . We take these sets to be the basis of the construction Definition 4.15 . A point x e X is called semistable if it lies in some X ...

Author: A.N. Parshin

Publisher: Springer Science & Business Media

ISBN: 3540546820

Category: Mathematics

Page: 286

View: 674

Two contributions on closely related subjects: the theory of linear algebraic groups and invariant theory, by well-known experts in the fields. The book will be very useful as a reference and research guide to graduate students and researchers in mathematics and theoretical physics.
Categories: Mathematics

Algebraic Geometry Sendai 1985

Algebraic Geometry  Sendai  1985

Tadao Oda. Ysa :: : I1«f QA Algebraic geometry, Sendai, 1985 / 564 edited by.

Author: Tadao Oda

Publisher: Elsevier Science Limited

ISBN: UOM:49015001310029

Category: Commutative algebra

Page: 794

View: 908

This guide to algebraic geometry covers the active areas of the subject: birational geometry of higher dimensional algebraic varieties, Kauml;hler manifolds and analytic varieties, abelian varieties, arithmetic algebraic geometry, rigid analytic spaces, cycles and vector bundles on algebraic varieties, mixed Hodge structures, period maps for K3 surfaces and for isolated singularities. Many of the papers not only contain original results, but also survey the particular topics covered.
Categories: Commutative algebra

Selected Topics in Algebraic Geometry II

Selected Topics in Algebraic Geometry   II

Algebraic Numbers. 1923. 96 pages. $1.50. Bulletin 62. Algebraic Numbers. II. 1928. Ill pages. $1.50. Bulletin 63. Selected Topics in Algebraic Geometry. 1928. 396 pages. $4.00. (Cloth, $4.50.) Bulletin 96. Selected Topics in Algebraic ...

Author: National Research Council (U.S.). Committee on Rational Transformations

Publisher:

ISBN: UOM:39015075081789

Category: Geometry, Algebraic

Page: 84

View: 439

Categories: Geometry, Algebraic

Combinatorial Algebraic Geometry

Combinatorial Algebraic Geometry

Combinatorial algebraic geometry is a field that, by design, straddles mathematical boundaries. One aim is to study algebraic varieties with special combinatorial features. At its roots, this field is about systems of polynomial ...

Author: Gregory G. Smith

Publisher: Springer

ISBN: 9781493974863

Category: Mathematics

Page: 390

View: 759

This volume consolidates selected articles from the 2016 Apprenticeship Program at the Fields Institute, part of the larger program on Combinatorial Algebraic Geometry that ran from July through December of 2016. Written primarily by junior mathematicians, the articles cover a range of topics in combinatorial algebraic geometry including curves, surfaces, Grassmannians, convexity, abelian varieties, and moduli spaces. This book bridges the gap between graduate courses and cutting-edge research by connecting historical sources, computation, explicit examples, and new results.
Categories: Mathematics

Basic Algebraic Geometry 1

Basic Algebraic Geometry 1

Algebraic geometry played a central role in 19th century math. The deepest results of Abel, Riemann, Weierstrass, and many of the most important works of Klein and Poincaré were part of this subject. The turn of the 20th century saw a ...

Author: Igor R. Shafarevich

Publisher: Springer Science & Business Media

ISBN: 9783642379567

Category: Mathematics

Page: 310

View: 791

Shafarevich's Basic Algebraic Geometry has been a classic and universally used introduction to the subject since its first appearance over 40 years ago. As the translator writes in a prefatory note, ``For all [advanced undergraduate and beginning graduate] students, and for the many specialists in other branches of math who need a liberal education in algebraic geometry, Shafarevich’s book is a must.'' The third edition, in addition to some minor corrections, now offers a new treatment of the Riemann--Roch theorem for curves, including a proof from first principles. Shafarevich's book is an attractive and accessible introduction to algebraic geometry, suitable for beginning students and nonspecialists, and the new edition is set to remain a popular introduction to the field.
Categories: Mathematics

Algebraic Geometry

Algebraic Geometry

I was influenced by Lang ( 16 ) in systematically using the Extension Theorem , in the pure commutative algebra as well as in the geometric applications . Because of this decision , some proofs have an unnecessary assumption that a ring ...

Author: J. S. Milne

Publisher: Allied Publishers

ISBN: 8177644548

Category: Geometry, Algebraic

Page: 260

View: 694

Categories: Geometry, Algebraic

Lectures on Algebraic Geometry I

Lectures on Algebraic Geometry I

The two volumes together are meant to serve as an introduction into modern algebraic geometry. But about two thirds of this first volume concern homological algebra, cohomology of groups, cohomology of sheaves and algebraic topology.

Author: Günter Harder

Publisher: Springer Science & Business Media

ISBN: 9783834883308

Category: Mathematics

Page: 301

View: 913

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 algebraic geometry, but they are also fundamental for other branches of mathematics and of great interest in their own. In the last chapter of volume I these concepts are applied to the theory of compact Riemann surfaces. In this chapter the author makes clear how influential the ideas of Abel, Riemann and Jacobi were and that many of the modern methods have been anticipated by them. For this second edition the text was completely revised and corrected. The author also added a short section on moduli of elliptic curves with N-level structures. This new paragraph anticipates some of the techniques of volume II.
Categories: Mathematics