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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Leave a Reply Cancel reply Enter your comment here Page – On the vanishing of local homotopy groups for isolated singularities of complex spaces, J. More precisely, ind-schemes include into them inducing homotopy equivalences, but whatever. Positivity in algebraic geometry 2 Volume 49 of Ergebnisse der Mathematik und ihrer Grenzgebiete: For example, the intersection multiplicity of two distinct complex curves which meet at a point in a complex algebraic surface S is always positive.

Demailly’s book and other book will get you reasonably up to speed on the line-bundle side of things. By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. Sign up using Facebook. Both volumes are also available as hardcover edition as Vols. About Why you should care about positivity Core traveling library Book: Post was not sent – check your email addresses! Other editions – View all Positivity in algebraic geometry 2 R.

Read, highlight, and take notes, across web, tablet, and phone. The proof of the Kodaira embedding theorem positivjty 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.

So if somebody can give any intuition about that word, it will be useful.

### Positivity in algebraic geometry. – Mathematics Stack Exchange

IIRobert Lazarsfeld. Positivity in Algebraic Geometry I: Account Options Sign in. Notify me of new comments via email.

You are commenting using your Facebook account. Some Applications of Multiplier Ideals. Line Bundles and Linear Series.

### Why you should care about positivity | Geometry Bulletin Board

The existing answers are good but according to me there is some analytic bias on display! This is the Kodaira embedding theorem.

Ample and Nef Line Bundles. Positivity in algebraic geometry. The details form a vast area of research that’s still being worked on.

## Positivity in Algebraic Geometry reading seminar (Fall 2016)

Because of some very nice Bochner-type formulas, positivity of this form implies the vanishing lazaarsfeld some cohomology groups. Extending things to vector bundles is still largely work in progress. Anthony Bordg 1 9. This site uses cookies.

To find out more, including how to control cookies, see here: This is completely false in topology: A summary of activity on several fronts Greenblatt on Wiseman’s “At Berkeley” How to teach someone how to prove something: The title might sound, on the face of it, like something specialized or technical. 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.

You are commenting using your WordPress. In my opinion, the Kodaira embedding theorem is one of the main reasons why the notion of positivity is so useful. Email required Address never made public. They have a great deal of relevant information. Account Options Sign in. My library Help Advanced Book Search. 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.

Ample and Nef Vector Bundles. Email Required, but never shown. Positivity in algebraic geometry 2 R.