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Asymptotic cohomological functions on projective varieties
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 128, Number 6, December 2006
- pp. 1475-1519
- 10.1353/ajm.2006.0044
- Article
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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.