Books in Algebraic geometry

Computational Morphology

1st Edition
Volume 6
June 28, 2014
G.T. Toussaint
English
eBook
9 7 8 1 4 8 3 2 9 6 7 2 2

Computational Geometry is a new discipline of computer science that deals with the design and analysis of algorithms for solving geometric problems. There are many areas of study in different disciplines which, while being of a geometric nature, have as their main component the extraction of a description of the shape or form of the input data. This notion is more imprecise and subjective than pure geometry. Such fields include cluster analysis in statistics, computer vision and pattern recognition, and the measurement of form and form-change in such areas as stereology and developmental biology.This volume is concerned with a new approach to the study of shape and form in these areas. Computational morphology is thus concerned with the treatment of morphology from the computational geometry point of view. This point of view is more formal, elegant, procedure-oriented, and clear than many previous approaches to the problem and often yields algorithms that are easier to program and have lower complexity.

Algebraic Geometry and Commutative Algebra

1st Edition
May 10, 2014
Hiroaki Hijikata + 2 more
English
eBook
9 7 8 1 4 8 3 2 6 5 0 5 6

Algebraic Geometry and Commutative Algebra in Honor of Masayoshi Nagata presents a collection of papers on algebraic geometry and commutative algebra in honor of Masayoshi Nagata for his significant contributions to commutative algebra. Topics covered range from Weierstrass models and endomorphism algebras of abelian varieties to the generic Torelli theorem for hypersurfaces in compact irreducible hermitian symmetric spaces. Coarse moduli spaces for curves are also discussed, along with discriminants of curves of genus 2 and arithmetic surfaces. Comprised of 14 chapters, this volume begins by describing a basic fibration as a Weierstrass model, with emphasis on elliptic threefolds with a section. The reader is then introduced to canonical bundles of analytic surfaces of class VII0 with curves; Lifting Problem on ideal-adically complete noetherian rings; and the canonical ring of a curve. Subsequent chapters deal with algebraic surfaces for regular systems of weights; elementary transformations of algebraic vector bundles; the irreducibility of the first differential equation of Painlevé; and F-pure normal rings of dimension two. The book concludes with an assessment of the existence of some curves. This monograph will be a useful resource for practitioners and researchers in algebra and geometry.

Saks Spaces and Applications to Functional Analysis

1st Edition
Volume 28
October 10, 2011
Barry J. Cooper
English
eBook
9 7 8 0 0 8 0 8 7 1 3 9 4

Introduction to Banach Spaces and their Geometry

1st Edition
Volume 68
October 10, 2011
B. Beauzamy
English
eBook
9 7 8 0 0 8 0 8 7 1 7 9 0

Real Elliptic Curves

1st Edition
Volume 54
August 18, 2011
N.L. Alling
English
eBook
9 7 8 0 0 8 0 8 7 1 6 5 3

Geometric Computations with Interval and New Robust Methods

1st Edition
December 1, 2003
H Ratschek + 1 more
English
eBook
9 7 8 0 8 5 7 0 9 9 5 1 8

This undergraduate and postgraduate text will familiarise readers with interval arithmetic and related tools to gain reliable and validated results and logically correct decisions for a variety of geometric computations plus the means for alleviating the effects of the errors. It also considers computations on geometric point-sets, which are neither robust nor reliable in processing with standard methods. The authors provide two effective tools for obtaining correct results: (a) interval arithmetic, and (b) ESSA the new powerful algorithm which improves many geometric computations and makes them rounding error free.

Power Geometry in Algebraic and Differential Equations

1st Edition
Volume 57
August 3, 2000
A.D. Bruno
English
eBook
9 7 8 0 0 8 0 5 3 9 3 3 1

The geometry of power exponents includes the Newton polyhedron, normal cones of its faces, power and logarithmic transformations. On the basis of the geometry universal algorithms for simplifications of systems of nonlinear equations (algebraic, ordinary differential and partial differential) were developed.The algorithms form a new calculus which allows to make local and asymptotical analysis of solutions to those systems.The efficiency of the calculus is demonstrated with regard to several complicated problems from Robotics, Celestial Mechanics, Hydrodynamics and Thermodynamics. The calculus also gives classical results obtained earlier intuitively and is an alternative to Algebraic Geometry, Differential Algebra, Lie group Analysis and Nonstandard Analysis.

Groups - Modular Mathematics Series

1st Edition
July 1, 1994
Camilla Jordan + 1 more
English
Paperback
9 7 8 0 3 4 0 6 1 0 4 5 9
eBook
9 7 8 0 0 8 0 5 7 1 6 5 2

This text provides an introduction to group theory with an emphasis on clear examples. The authors present groups as naturally occurring structures arising from symmetry in geometrical figures and other mathematical objects. Written in a 'user-friendly' style, where new ideas are always motivated before being fully introduced, the text will help readers to gain confidence and skill in handling group theory notation before progressing on to applying it in complex situations. An ideal companion to any first or second year course on the topic.