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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This map is then algebraic. Account Options Sign in.

Much of algebraic geometry builds on this kind of rigidity. This is a great point of view.

Positivity in Algebraic Geometry I: Home Questions Tags Users Unanswered. The proof of the Kodaira embedding theorem in Griffiths and Harris uses the Kodaira vanishing theorem alluded to by Zach, which is an example of the kinds of vanishing theorems that you are reading about.


Positivity in Algebraic Geometry reading seminar (Fall 2016)

Anthony Bordg 1 9. And those are often easy to compute using iterations of short exact sequences. Both volumes are also available posifivity hardcover edition as Vols. 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. Read, highlight, and take notes, across web, tablet, and phone.

Positivity in algebraic geometry 2 – R.K. Lazarsfeld, University of Michigan Staff – Google Books

Line Bundles and Linear Series. So if somebody can give any intuition about that word, it will be useful.

Post was not sent – check your email addresses! Positivity in algebraic geometry 2 Volume 49 of Ergebnisse der Mathematik gwometry ihrer Grenzgebiete: I Volume 2 of Positivity in Algebraic Geometry: The point of line bundles which are positive in various senses is that they are the ones which have a chance of having sections, hence yielding some kind of map out of your variety.


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Positivity in Algebraic Geometry II

Line Bundles and Linear Series. Contents Ample and Nef Vector Bundles. Contents Ample and Nef Line Bundles. Demailly’s book and other book will get you reasonably up to speed on the line-bundle side of things. Post as a guest Name.

Sign up using Email and Password. The details form a vast area of research that’s still being worked on. In my opinion, the Kodaira embedding theorem is one of the main reasons why the notion of positivity is so useful. No eBook available Springer Shop Amazon. Lazarsfeld No preview available – Lazarsfeld Limited preview – Let’s verify that the Kodaira embedding theorem holds for line bundles on curves.

Because of some very nice Bochner-type formulas, positivity of this form implies the vanishing of some cohomology groups.