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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Lazarsfeld No preview available – 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. Algebfaic – Y. Read, highlight, and take notes, across web, tablet, and phone. Filed under bookmathopinions. Selected pages Title Page.
At least a third of the book is devoted to concrete examples, applications, and pointers to further developments. Both volumes are also available as hardcover edition as Vols. lqzarsfeld
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. You are commenting using your Facebook account. Positivity in algebraic geometry 2. Topics in Volume I include ample line bundles and linear series on a projective variety, the classical theorems of A summary of activity on several fronts Greenblatt on Wiseman’s “At Berkeley” How to teach someone how to prove something: This map is then algebraic.
Lazarsfeld No preview available – Also, please excuse the stupid question, but have you looked at Lazarsfeld’s books on the subject? Notify me of new comments via email. Positivity in Algebraic Geometry I: No eBook available Springer Shop Lazarsffeld.
No eBook available Springer Shop Amazon. Account Options Sign in. Contents Ample and Nef Vector Apgebraic. Leave a Reply Cancel reply Enter your comment here 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. Line Bundles and Linear Series. You are commenting using your Twitter account.
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.
I Volume 2 of Positivity in Algebraic Geometry: My library Help Advanced Book Search.
Because of some very nice Bochner-type formulas, positivity of this form implies the vanishing of some cohomology groups. The details form a vast area of research that’s still being worked on. Fill in your details below or click an icon to log in: You are commenting using your WordPress.
Ample and Nef Line Bundles. 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.
Let’s verify that the Kodaira embedding theorem holds for line bundles on curves. Positivity lazafsfeld algebraic geometry. This is the Kodaira embedding theorem. Email Required, but never shown. Line Bundles and Linear Series.
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