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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For example, the intersection multiplicity of two distinct complex curves which meet at a point in a complex algebraic surface S is always positive. 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.
Lazarsfeld Limited preview – Extending things to vector bundles is still largely work in progress. 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. April algebraix, at 1: This two volume work on “Positivity in Algebraic Geometry” contains a contemporary account of a body of work in algebrwic algebraic geoometry loosely centered around the theme of positivity.
Why you should care about positivity | Geometry Bulletin Board
Whereas Volume I is more elementary, the present Volume II is more at the research level and somewhat more specialized. And those are often easy to compute using iterations of short exact sequences. Selected pages Title Page. Positivity in Algebraic Geometry I: Account Options Sign in. Lazarsfeld No preview available – This map is then algebraic.
Selected pages Title Page. A summary of activity on several fronts Greenblatt on Wiseman’s “At Berkeley” How xlgebraic teach someone how to prove something: 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. Geometric Properties of Ample Bundles. Page – Y.
Line Bundles and Linear Series. Fill in your details below or click an icon to log algebeaic More precisely, ind-schemes include into them inducing homotopy equivalences, but whatever. This is the Kodaira embedding theorem. Post was not sent – check your email addresses!
By continuing to use this website, you agree to their use. Topics in Volume I include ample line bundles and linear series on a projective variety, the classical theorems of Notify me of new comments via email. The existing answers are good but according to me there is some analytic bias on display! Topics in Volume I include ample line bundles and linear series on a projective variety, the classical theorems of You are commenting using your WordPress.
The title might sound, on the face of it, like something specialized or technical.
Positivity in Algebraic Geometry I: 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.
Positivity in Algebraic Geometry II
Because of some very nice Bochner-type formulas, positivity of this form implies the vanishing of some cohomology groups.