Classification Theory of Polarized Varieties

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Paperback | 22 October 1990

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220 Pages

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A polarised variety is a modern generalization of the notion of a variety in classical algebraic geometry. It consists of a pair: the algebraic variety itself, together with an ample line bundle on it. Using techniques from abstract algebraic geometry that have been developed over recent decades, Professor Fujita develops classification theories of such pairs using invariants that are polarised higher-dimensional versions of the genus of algebraic curves. The heart of the book is the theory of D-genus and sectional genus developed by the author, but numerous related topics are discussed or surveyed. Proofs are given in full in the central part of the development, but background and technical results are sometimes just sketched when the details are not essential for understanding the key ideas. Readers are assumed to have some background in algebraic geometry, including sheaf cohomology, and for them this work will provide an illustration of the power of modern abstract techniques applied to concrete geometric problems. Thus the book helps the reader not only to understand about classical objects but also modern methods, and so it will be useful not only for experts but also non-specialists and graduate students.

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"...readable, very useful book. This book belongs in the library of every geometer." Andrew J. Sommese, Bulletin of the American Mathematical Society

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You Can Find This Book In

Non-Fiction Mathematics Geometry Algebraic Geometry Applied Mathematics Topology

Introduction
Delta-genus and the hyperplane section method
Sectional genus and adjoint bundles
Related topics
Varieties of small degrees
Varieties of small codimension
Varieties of small secant varieties
Varieties with many lines
Hyperelliptic polarised varieties
Castelnuovo bounds and Castelnuovo varieties
Ample vector bundles with small invariants
Background information
Computer constructed classification of polarised varieties
Table of Contents provided by Publisher. All Rights Reserved.

Classification Theory of Polarized Varieties

At a Glance

Paperback

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

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