Asymptotic cohomological functions on projective varieties

By Alex Kuronya. 2005

55 citations recorded by the source corpus.

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 Neron-Severi space. To illustrate the theory, we work out these invariants for abelian varieties, smooth surfaces, and certain homogeneous spaces.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7dc2df35d3e44d3a24782106d96c033ff92344db

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In Geometry and Topology

1. B. Totaro
2. Sam Payne
3. Max Lieblich
4. Philipp Gross
5. Fabio Nironi
6. Y. Félix
7. N. Perrin
8. Stefan Schreieder

In Mathematical Physics

1. B. Totaro
2. Sam Payne
3. Y. Félix
4. Max Lieblich
5. Fabio Nironi
6. Philipp Gross
7. N. Perrin
8. W. Ziller

Citations in the corpus

• Line bundles with partially vanishing cohomology (2010, background): “The first is about the relation between q-ampleness and Küronya’s asymptotic cohomological functions [19].”