Asymptotic Cohomological Functions on Projective Varieties

We consider certain cohomological invariants called asymptotic cohomological functions, which are associated to irreducible projective varieties. Asymptotic cohomological functions are generalizations of the concept of the volume of a line bundle--the asymptotic growth of the number of global sectio...

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Bibliographic Details
Published in:American journal of mathematics 2006-12, Vol.128 (6), p.1475-1519
Main Author: Küronya, Alex
Format: Article
Language:English
Subjects:
Algebra
Algebraic geometry
Asymptotic methods
Continuous functions
Exact sciences and technology
Integers
Mathematical functions
Mathematical models
Mathematical problems
Mathematical theorems
Mathematical triviality
Mathematics
Numerical analysis
Polynomials
Sciences and techniques of general use
Smooth surfaces
Vector spaces
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Summary:We consider certain cohomological invariants called asymptotic cohomological functions, which are associated to irreducible projective varieties. Asymptotic cohomological functions are generalizations of the concept of the volume of a line bundle--the asymptotic growth of the number of global sections--to higher cohomology. We establish that they give a notion invariant under the numerical equivalence of divisors, and extend uniquely to continuous functions on the real Néron-Severi space. To illustrate the theory, we work out these invariants for abelian varieties, smooth surfaces, and certain homogeneous spaces.
ISSN:0002-9327
1080-6377
1080-6377
DOI:10.1353/ajm.2006.0044