This two volume work on “Positivity in Algebraic Geometry” contains a contemporary account of a body of work in complex algebraic geometry loosely centered. Positivity in Algebraic Geometry I: Classical Setting: Line Bundles and Linear Series. Front Cover ยท R.K. Lazarsfeld. Springer Science & Business Media, Aug I started this blog about a year ago briefly recommending Rob Lazarsfeld’s book Positivity in Algebraic Geometry, which gives bite-size.

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They have a great deal of relevant information. Geometric Manifestations of Positivity. Positivity in Algebraic Geometry I: In fact, positivity is arguably the fundamental difference between algebraic geometry and topology.

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. IIRobert Lazarsfeld. Whereas Volume I is more elementary, the present Volume II is more at the research level and somewhat more specialized.

## Positivity in Algebraic Geometry II

This is because the Poincare dual of any single point is the volume form, which is certainly positive. Home Questions Lazarsreld Users Unanswered. Topics in Volume I include ample line bundles and linear series on a projective variety, the classical theorems of The title might sound, on the face of it, like something specialized or technical.

At least a third of the book is devoted to concrete examples, applications, and pointers to further developments.

This site uses cookies. Page – On the vanishing of local homotopy groups for isolated singularities of complex spaces, J. 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.

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.

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.

No eBook goemetry Springer Shop Amazon. Positivity in algebraic geometry 2 Ih. Geometric Properties of Ample Bundles. I learned about this from Griffiths and Harris, Chapter 1. Post Your Answer Discard By clicking “Post Your Answer”, you acknowledge that you have read our updated terms of serviceprivacy policy and cookie policyand that your continued use of the website is subject to these policies.

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### Positivity in Algebraic Geometry

Contents Ample and Nef Vector Bundles. Anthony Bordg 1 9. Sign up using Email and Password. The existing answers are good but according to me there is some analytic bias on display!

Sorry, your blog cannot share posts by email. For example, the intersection multiplicity of two distinct complex curves which meet at a point in a complex algebraic surface S is always positive. No eBook available Springer Shop Amazon. Selected pages Title Page. Positivity in algebraic geometry 2. Ample and Nef Vector Bundles. Positivity in algebraic geometry. But now there is a crazy alternative: A good deal of this material has not previously appeared in book form, and lazarwfeld parts are worked out here in detail for the first time.

Read, highlight, and take notes, across web, tablet, and phone. And those are often easy to compute using iterations of short exact sequences. Account Options Sign in. Positivity in algebraic geometry 2 Volume 49 of Ergebnisse der Mathematik und ihrer Grenzgebiete: Positivity in Algebraic Geometry I: The details form a vast area of research that’s still being worked on.

Let me describe one rather specialized example that has come my way. lazarzfeld

By clicking “Post Your Answer”, you acknowledge that you have read our updated terms of serviceprivacy policy and cookie policyand that your continued use of the website is subject to these policies. Account Options Sign in. Algebrqic 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.

Also, please excuse the stupid question, but have you looked at Lazarsfeld’s books on the subject?

This is the Kodaira embedding theorem.