Abstract

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.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 1475-1519
Launched on MUSE
2006-12-11
Open Access
No
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