Classification Theory of Polarized Varieties

by Takao Fujita

Overview

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 polarized 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 sketched in when the details are not essential for understanding the key ideas.

Product Details

ISBN-13:	9780521392020
Publisher:	Cambridge University Press
Publication date:	08/23/1990
Series:	London Mathematical Society Lecture Note Series , #155
Pages:	220
Product dimensions:	6.02(w) x 8.94(h) x 0.47(d)

Table of Contents

Introduction; 1. Δ-genus and the hyperplane section method; 2. Sectional genus and adjoint bundles; 3. Related topics; 4. Varieties of small degrees; 5. Varieties of small codimension; 6. Varieties of small secant varieties; 7. Varieties with many lines; 8. Hyperelliptic polarised varieties; 9. Castelnuovo bounds and Castelnuovo varieties; 10. Ample vector bundles with small invariants; Appendix 1: Background information; Appendix 2: Computer constructed classification of polarised varieties.

Editorial Reviews

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

From the Publisher