LAZARSFELD POSITIVITY IN ALGEBRAIC GEOMETRY PDF

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This two volume work on Positivity in Algebraic Geometry contains a contemporary account of a body of work in complex algebraic geometry loosely centered around the theme of positivity. 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.

Geometric Manifestations of Positivity. Vanishing Theorems. Local Positivity. Projective Bundles. Cohomology and Complexes. Glossary of Notation. Ample and Nef Line Bundles. Linear Series. B2 Complexes. Positivity in algebraic geometry 2 R.

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Positivity in Algebraic Geometry I

The main theme of this two volume monograph is a comprehensive description of the fields of complex algebraic geometry connected with the notion of positivity. The first volume in the set offers a systematic presentation of ideas connected with classical notions of linear series and ample divisors on a projective variety from a modern point of view. Individual chapters are devoted to the basic theory of positivity for line bundles and Castelnuovo-Mumford regularity, asymptotic geometry of linear systems, geometric properties of projective subvarieties of small codimension, vanishing theorems for divisors and the theory of local positivity. The second volume contains the second and the third parts of the monograph.

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Positivity in Algebraic Geometry I : Classical Setting: Line Bundles and Linear Series

This two volume work on "Positivity in Algebraic Geometry" contains a contemporary account of a body of work in complex algebraic geometry loosely centered around the theme of positivity. 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. Whereas Volume I is more elementary, the present Volume II is more at the research level and somewhat more specialized.

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By using our site, you acknowledge that you have read and understand our Cookie Policy , Privacy Policy , and our Terms of Service. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up. To expand a little on Gunnar's answer, I'll attempt to give you some intuition as to what positivity means in the context of embeddings of complex manifolds into projective space. This is because the Poincare dual of any single point is the volume form, which is certainly positive. There is a simple criterion we can use to test this.

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Positivity in Algebraic Geometry I. Classical Setting - Line Bundles and Linear Series

Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete. This two volume work on Positivity in Algebraic Geometry contains a contemporary account of a body of work in complex algebraic geometry loosely centered around the theme of positivity. 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.

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