Higher-Dimensional Geometry Over Finite Fields PDF Download

Author: D. Kaledin
Publisher: IOS Press
ISBN: 1607503255
Category : Mathematics
Languages : en
Pages : 356

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Book Description
Number systems based on a finite collection of symbols, such as the 0s and 1s of computer circuitry, are ubiquitous in the modern age. Finite fields are the most important such number systems, playing a vital role in military and civilian communications through coding theory and cryptography. These disciplines have evolved over recent decades, and where once the focus was on algebraic curves over finite fields, recent developments have revealed the increasing importance of higher-dimensional algebraic varieties over finite fields. The papers included in this publication introduce the reader to recent developments in algebraic geometry over finite fields with particular attention to applications of geometric techniques to the study of rational points on varieties over finite fields of dimension of at least 2.

Author: D. Kaledin
Publisher:
ISBN: 9781597344531
Category : Finite fields (Algebra)
Languages : en
Pages : 356

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Book Description
Number systems based on a finite collection of symbols, such as the 0s and 1s of computer circuitry, are ubiquitous in the modern age. Finite fields are the important number systems. This title introduces the reader to the developments in algebraic geometry over finite fields.

Author: Dmitri Kaledin
Publisher: IOS Press
ISBN: 1586038559
Category : Mathematics
Languages : en
Pages : 356

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"Proceedings of the NATO Advanced Study Institute on Higher-Dimensional Geometry over Finite Fields, Geottingen, Germany, 25 June-6 July 2007."--T.p. verso.

Author: James William Peter Hirschfeld
Publisher: Oxford University Press on Demand
ISBN: 9780198502951
Category : Law
Languages : en
Pages : 555

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Book Description
I. Introduction 1. Finite fields 2. Projective spaces and algebraic varieties II. Elementary general properties 3. Subspaces 4. Partitions 5. Canonical forms for varieties and polarities III. The line and the plane 6. The line 7. First properties of the plane 8. Ovals 9. Arithmetic of arcs of degree two 10. Arcs in ovals 11. Cubic curves 12. Arcs of higher degree 13. Blocking sets 14. Small planes Appendix Notation References.

Author: Thomas Peternell
Publisher: Birkhäuser
ISBN: 3034888937
Category : Mathematics
Languages : en
Pages : 221

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Book Description
This book is based on lecture notes of a seminar of the Deutsche Mathematiker Vereinigung held by the authors at Oberwolfach from April 2 to 8, 1995. It gives an introduction to the classification theory and geometry of higher dimensional complex-algebraic varieties, focusing on the tremendeous developments of the sub ject in the last 20 years. The work is in two parts, with each one preceeded by an introduction describing its contents in detail. Here, it will suffice to simply ex plain how the subject matter has been divided. Cum grano salis one might say that Part 1 (Miyaoka) is more concerned with the algebraic methods and Part 2 (Peternell) with the more analytic aspects though they have unavoidable overlaps because there is no clearcut distinction between the two methods. Specifically, Part 1 treats the deformation theory, existence and geometry of rational curves via characteristic p, while Part 2 is principally concerned with vanishing theorems and their geometric applications. Part I Geometry of Rational Curves on Varieties Yoichi Miyaoka RIMS Kyoto University 606-01 Kyoto Japan Introduction: Why Rational Curves? This note is based on a series of lectures given at the Mathematisches Forschungsin stitut at Oberwolfach, Germany, as a part of the DMV seminar "Mori Theory". The construction of minimal models was discussed by T.

Author: Károly Jr. Böröczky
Publisher: Springer Science & Business Media
ISBN: 3662051230
Category : Mathematics
Languages : en
Pages : 307

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Book Description
Exploring the connections between arithmetic and geometric properties of algebraic varieties has been the object of much fruitful study for a long time, especially in the case of curves. The aim of the Summer School and Conference on "Higher Dimensional Varieties and Rational Points" held in Budapest, Hungary during September 2001 was to bring together students and experts from the arithmetic and geometric sides of algebraic geometry in order to get a better understanding of the current problems, interactions and advances in higher dimension. The lecture series and conference lectures assembled in this volume give a comprehensive introduction to students and researchers in algebraic geometry and in related fields to the main ideas of this rapidly developing area.

Author: Fedor Bogomolov
Publisher: Springer
ISBN: 3319497634
Category : Mathematics
Languages : en
Pages : 267

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Book Description
Based on the Simons Symposia held in 2015, the proceedings in this volume focus on rational curves on higher-dimensional algebraic varieties and applications of the theory of curves to arithmetic problems. There has been significant progress in this field with major new results, which have given new impetus to the study of rational curves and spaces of rational curves on K3 surfaces and their higher-dimensional generalizations. One main recent insight the book covers is the idea that the geometry of rational curves is tightly coupled to properties of derived categories of sheaves on K3 surfaces. The implementation of this idea led to proofs of long-standing conjectures concerning birational properties of holomorphic symplectic varieties, which in turn should yield new theorems in arithmetic. This proceedings volume covers these new insights in detail.

Author: J. Scott Carter
Publisher: World Scientific
ISBN: 9789810220662
Category : Science
Languages : en
Pages : 344

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Book Description
This marvelous book of pictures illustrates the fundamental concepts of geometric topology in a way that is very friendly to the reader. It will be of value to anyone who wants to understand the subject by way of examples. Undergraduates, beginning graduate students, and non-professionals will profit from reading the book and from just looking at the pictures.

Author: Gary L. Mullen
Publisher: CRC Press
ISBN: 1439873828
Category : Computers
Languages : en
Pages : 1048

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Book Description
Poised to become the leading reference in the field, the Handbook of Finite Fields is exclusively devoted to the theory and applications of finite fields. More than 80 international contributors compile state-of-the-art research in this definitive handbook. Edited by two renowned researchers, the book uses a uniform style and format throughout and

Author:
Publisher:
ISBN: 9781109392982
Category : Finite fields (Algebra)
Languages : en
Pages :

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This thesis is primarily concerned with specific types of spreads of three-dimensional and five-dimensional projective geometries over finite fields. Spreads are a partition of a projective geometry, and are used to construct translation planes through the Andre/Bruck-Bose construction. This thesis uses the Bruck-Bose model, which is more geometric in nature. The types of spreads examined include the following: spreads of five-dimensional projective geometries for three-dimensional flag-transitive affine planes, polarity-paired spreads of three-dimensional projective geometries, and spreads of five-dimensional projective geometries constructed from a three-dimensional circle geometry. In the introduction to the thesis, a short historical account is given of some aspects of modern incidence geometry. Specifically, a partial history of the theory of projective and affine planes that leads to the study of translation planes. In Chapters Two and Three the definitions of a projective plane and translation plane are given, along with properties of these objects that will be useful in their study. Also the classical (Desarguesian) projective plane and the classical projective geometries are defined. It is these higher-dimensional Desarguesian geometries that are needed for the Bruck-Bose model of translation planes. The Andre/Bruck-Bose construction is explained in Chapter Four. This includes a discussion of the Miquelian inversive plane, which can be used to model a fundamental family of spreads called "regular". In Chapter Five spreads of five-dimensional projective geometries are used to construct odd order three-dimensional flag-transitive affine planes. This involves examining the way that planes in the spread intersect a partition of a five-dimensional geometry. Chapter Six is concerned with polarities of three-dimensional geometries applied to spreads of that geometry, leading to the concept of polarity-paired spreads. The symplectic polarity-paired spreads are used to construct a certain class of ovoids of a specific generalized quadrangle. In Chapter Seven a three-dimensional circle geometry is used to construct spreads of five-dimensional projective geometries. This circle geometry and spreads constructed from a regular spread mirror the concept of the Miquelian inversive plane and its relationship to subregular spreads from a regular spread of a three-dimensional projective geometry. Finally, the possibility of further work is discussed in Chapter Eight.