Geometry in advanced pure mathematics

by Bullett, Shaun Fearn, T. Smith, F. T., (Frank T.)

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Title Statements

Full title :Geometry in advanced pure mathematics / editors, Shaun Bullett (Queen Mary University of London, UK), Tom Fearn (University College London, UK), Frank Smith (University College London, UK).

Summary

"This book leads readers from a basic foundation to an advanced level understanding of geometry in advanced pure mathematics. Chapter by chapter, readers will be led from a foundation level understanding to advanced level understanding. This is the perfect text for graduate or PhD mathematical-science students looking for support in algebraic geometry, geometric group theory, modular group, holomorphic dynamics and hyperbolic geometry, syzygies and minimal resolutions, and minimal surfaces. Geometry in Advanced Pure Mathematics is the fourth volume of the LTCC Advanced Mathematics Series. This series is the first to provide advanced introductions to mathematical science topics to advanced students of mathematics. Edited by the three joint heads of the London Taught Course Centre for PhD Students in the Mathematical Sciences (LTCC), each book supports readers in broadening their mathematical knowledge outside of their immediate research disciplines while also covering specialized key areas."--Publisher's website.

Edition Statements

Publication Date:©2017

Publication Statements

Publisher(s):World Scientific Publishing Europe Ltd
Place of Publication:London
Language:eng
Publication Date:©2017

The Physical Object

Description:1 online resource : : illustrations

Edition Identifiers

ISBN:9781786341082, 1786341085, 9781786341099, 1786341093
oclc:ocn981957261
LC Classification:QA564
Dewey Decimal:516.3/5

Preface; Chapter 1. Algebraic Geometry; 1. Introduction; 1.1. Solving polynomial equations; 1.2. Historical development; 2. Varieties and Schemes; 2.1. Affine varieties ; 2.2. Morphisms; 2.3. Sheaves; 2.4. Schemes; 2.5. Projective varieties; 2.6. First properties of schemes; 3. Local Properties; 3.1. Non-singular schemes; 3.2. Multiplicities; 3.3. Divisors; 3.4. Riemann{Roch theorem; 4. Weil Conjectures; 4.1. The zeta function; 4.2. Rationality for curves; 4.3. Cohomological interpretation of Weil conjectures; 5. Further Reading; 6. Exercises

6.1. Solutions and hints to selected exercises; References; Chapter 2. Introduction to the Modular Group and Modular Forms; 1. Introduction to the Main Characters; 1.1. Prologue; 1.2. The modular group and Möbius transformations in the plane; 1.3. Hyperbolic geometry in the upper half-plane; 1.4. The upper half-plane as parameter space: Lattices in the plane; 1.5. Geometry of real Möbius transformations; 1.6. Exercises for Section 1; 2. Discontinuity of the Group Action: The Modular Surface; 2.1. Fundamental sets for discrete groups; 2.2. A fundamental domain for SL(2, Z)

4.5. Diophantine approximation of irrational numbers; 4.6. The Farey …

Subjects

Algebraische Geometrie Geometrie Géométrie algébrique Géométrie hyperbolique Geometrische Gruppentheorie geometry Geometry, Algebraic Geometry, Hyperbolic MATHEMATICS -- Geometry Minimalfläche