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 · 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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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.
No eBook available Springer Shop Amazon. 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.
Also, please excuse the stupid question, but have you looked at Lazarsfeld’s geomety on the subject?
By continuing to use this website, you agree to their use. The proof positiviity 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.
At least a third of the book is devoted to concrete examples, applications, and pointers to further developments. Home Questions Tags Users Unanswered.
Positivity in Algebraic Geometry reading seminar (Fall 2016)
Topics in Volume I include ample line bundles and linear series on a projective variety, the classical theorems of Selected pages Title Page. Positivity in algebraic geometry 2. My library Help Advanced Book Search. Email required Address never made public.
Geometric Manifestations of Positivity.
To find out more, including how to control cookies, see here: This is because the Poincare dual of any single point is the volume form, which is certainly positive. The title might sound, on the face of it, like something specialized or technical. For example, the intersection multiplicity of two distinct complex curves which meet at a point in a complex algebraic surface S is always positive.
Positivity in Algebraic Geometry I: The details form a vast area of research that’s still being worked on.
Positivity in algebraic geometry 2 R. The existing answers are good but according to me there is some analytic bias on display!
Positivity in Algebraic Geometry II
At least a third of the book is devoted to concrete examples, applications, and pointers to further developments. There is a simple criterion we can use to test this.
Positivity in algebraic geometry. – Mathematics Stack Exchange
I learned about this from Griffiths and Harris, Chapter 1. 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. Line Bundles and Linear Series R. This is apgebraic Kodaira embedding theorem.
Why you should care about positivity | Geometry Bulletin Board
Much of algebraic geometry builds on this kind of rigidity.