Derivative complex, BGG correspondence, and numerical inequalities for compact Kähler manifolds

Details Derivative complex, BGG correspondence, and numerical inequalities for compact Kähler manifolds Derivative complex, BGG correspondence, and numerical inequalities for compact Kähler manifolds

2009-07-03

arxiv.org/abs/0907.0651v2

Mathematics

Algebraic Geometry

21 pages; substantial changes to the exposition, title changed, and some new material added; final version to appear in Invent

Scientific paper

The cohomology algebra of the canonical bundle of a compact K\"ahler manifold is naturally viewed as a module over an exterior algebra. We use the Bernstein-Gel'fand-Gel'fand correspondence, together with Generic Vanishing theory, in order to understand the regularity properties of this module. We also relate it to the infinitesimal theory of the canonical linear series inside paracanonical space. Finally, we apply vector bundle methods on the polynomial ring side to obtain inequalities for the holomorphic Euler characteristic and the Hodge numbers of compact K\"ahler manifolds without irregular fibrations.

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