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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Read, highlight, and take notes, across web, tablet, and phone. Fill in your details below or click an icon to log in: 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)

Also, please excuse the stupid question, but have you looked at Lazarsfeld’s books on the subject? Sorry, your blog cannot share posts by email. Both volumes are also available as hardcover edition as Vols.

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Anthony Bordg 1 9. Lazarsfeld No preview available – For example, the intersection multiplicity of two distinct complex curves which meet at a point in a complex algebraic surface S is always positive. Extending things to vector bundles is still largely work in progress. This site uses cookies. 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.

Positivity in algebraic geometry 2 R. Whereas Volume I is more elementary, the present Volume II is more at the research level and somewhat more specialized. Email Required, but never shown. 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.

Positivity for Vector Bundles, and Multiplier Ideals. Line Bundles and Linear Series. A summary of activity on several fronts Greenblatt on Wiseman’s “At Berkeley” How to teach someone how to prove something: This is a great point of view.

Positivity in algebraic geometry. – Mathematics Stack Exchange

Post was not sent – check your email addresses! Ample and Nef Vector Bundles. To find out more, including how to control cookies, see here: So if somebody can give any intuition about that word, it will be useful. The title might sound, on the face of it, like something specialized or technical.


About Why you should care about positivity Core traveling library Book: Popular passages Page – Griffiths, Hermitian differential geometry and the theory of positive lazarsfele ample holomorphic vector bundles, J.

Mathematics Stack Exchange works best with JavaScript enabled. This map is then algebraic. Note that this applies to varieties in positive characteristic too! A geoketry deal of this material has not previously appeared in book form, and substantial parts are worked out here in detail for the first time. Lazarsfeld No preview available – And those are often easy to compute using iterations of short exact sequences.