Asymptotic cohomological functions on projective varieties

Details Asymptotic cohomological functions on projective varieties Asymptotic cohomological functions on projective varieties

2005-01-27

arxiv.org/abs/math/0501491v1

Mathematics

Algebraic Geometry

32 pages, 3 figures

Scientific paper

In this paper we define certain analogues of the volume of a divisor - called asymptotic cohomological functions - and investigate their behaviour on the Neron--Severi space. We establish that asymptotic cohomological functions are invariant with respect to the numerical equivalence of divisors, and that they give rise to continuous functions on the real Neron--Severi space. To illustrate the theory, we work out these invariants for abelian varieties, smooth surfaces, and certain homogeneous spaces.

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