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: Lazarsfeld, R.
: Positivity in Algebraic Geometry. Vol. I. Classical Setting: Line Bundles and Linear Series; Vol.II. Positivity for Vector Bundles, and Multiplier Ideals
: Springer
: 2004
ISBN: 978354022587 (Vol.I); 9783540225317 (Vol.II)
: A Series of Modern Surveys in Mathematics
: English
: pdf
: 5,4 mb
: 387+385

Topics in Volume I include ample line bundles and linear series on a projective variety, the classical theorems of Lefschetz and Bertini and their modern outgrowths, vanishing theorems, and local positivity. Volume II begins with a survey of positivity for vector bundles, and moves on to a systematic development of the theory of multiplier ideals and their applications. A good deal of this material has not previously appeared in book form, and substantial parts are worked out here in detail for the first time. At least a third of the book is devoted to concrete examples, applications, and pointers to further developments.

Volume I is more elementary than Volume II, and, for the most part, it can be read without access to Volume II.


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