• Title: Classical Algebraic Geometry: A Modern View
• Author(s) Igor V. Dolgachev
• Publisher: Cambridge University Press; 1st edition (October 8, 2012)
• Hardcover: 647 pages
• eBook: PDF (722 pages, 3.1 MB) and ePub
• Language: English
• ISBN-10: 1107017653
• ISBN-13: 978-3642725494
• Share This:  

Book Description

The main purpose of the present treatise is to give an account of some of the topics in algebraic geometry which while having occupied the minds of many mathematicians in previous generations have fallen out of fashion in modern times.

This detailed exposition makes the rich legacy of classical algebraic geometry accessible to modern algebraic geometers and to others who are interested in applying classical results. Topics include plane algebraic curves of low degree, special algebraic surfaces, theta functions and Cremona transformations.

• Igor V. Dolgachev is Professor Emeritus in the Department of Mathematics at the University of Michigan.

• Amazon

• Geometry and Topology
• Computer Graphics
• Computational and Algorithmic Mathematics
• Applied Mathematics

• Classical Algebraic Geometry: A Modern View (Igor V. Dolgachev)
• The Mirror Site (1) - PDF

• Metric Algebraic Geometry (Paul Breiding, et al)

  This book combines concepts from algebraic geometry and differential geometry. Building on classical foundations. Many applied problems center around metric questions, such as optimization with respect to distances.

• Convex Bodies and Algebraic Geometry: Theory of Toric Varieties

  This book is an accessible introduction to current algebraic geometry of toric varieties gives new insight into continued fractions as well as their higher-dimensional analogues, the isoperimetric problem and other questions on convex bodies.

• Algorithms in Real Algebraic Geometry (Saugata Basu, et al)

  The monograph gives a self-contained detailed exposition of the algorithmic real algebraic geometry. It will be useful both for beginners and for advanced readers, who work in real algebraic geometry or apply its methods in other fields.

• Sheaf Theory through Examples (Daniel Rosiak)

  Taking an applied category theory perspective, this book provides an approachable introduction to elementary sheaf theory and examines applications. It seeks to bridge the powerful results of sheaf theory as used by mathematicians and real-world applications.

• Spectral Geometry of Partial Differential Operators

  The aim of Spectral Geometry of Partial Differential Operators is to provide a basic and self-contained introduction to the ideas underpinning spectral geometric inequalities arising in the theory of partial differential equations.

• Differential Geometry: From Elastic Curves to Willmore Surfaces

  This open access book covers the main topics for a course on the differential geometry of curves and surfaces. There is a strong focus on variational problems, ranging from elastic curves to surfaces that minimize area, or the Willmore functional.

• Discrete Differential Geometry (Alexander I. Bobenko)

  An emerging field of Discrete Differential Geometry (DDG) aims at the development of discrete equivalents of notions and methods of classical differential geometry. No knowledge of differential geometry is expected.

• Spectral Geometry of Graphs (Pavel Kurasov)

  This open access book gives a systematic introduction into the Spectral Theory of Differential Operators on metric graphs. Main focus is on the fundamental relations between the spectrum and the geometry of the underlying graph.

• New Directions in Geometric and Applied Knot Theory

  The aim of this book is to present recent results in both theoretical and applied Knot Theory - which are at the same time stimulating for leading researchers in the field as well as accessible to non-experts.