Hidden Bibliographic Details
| Other title: | Polarized varieties.
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| ISBN: | 9781107361645
1107361648
9780511662638
0511662637
0521392020
9780521392020
1139884573
9781139884570
1107366550
9781107366558
1107371244
9781107371248
1107370108
9781107370104
1299404316
9781299404311
1107364094
9781107364097
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| Notes: | Includes bibliographical references (pages 184-201) and index.
English.
Print version record.
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| Summary: | 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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| Other form: | Print version: Fujita, Takao. Classification theories of polarized varieties. Cambridge ; New York : Cambridge University Press, 1990 0521392020
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