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- W2041403874 abstract "Given an irregular compact Kahler manifold X, one can form the derivative complex of X, which governs the deformation theory of the groups H i(X,α) as α varies over Pic(X). Together with its variants, it plays a central role in a body of work involving generic vanishing theorems. The purpose of this paper is to present two new applications of this complex. First, we show that it fits neatly into the setting of the so-called Bernstein-Gel’fand-Gel’fand (BGG) correspondence between modules over an exterior algebra and linear complexes over a symmetric algebra (cf. [BGG], [EFS], [Eis], [Co]). What comes out here is that some natural cohomology modules associated to X have a surprisingly simple algebraic structure, and that conversely one can read off from these modules some basic geometric invariants associated to the Albanese mapping of X. Secondly, under an additional hypothesis, the derivative complex determines a vector bundle on the projectivized tangent space to Pic(X) at the origin. We show that this bundle, which encodes the infinitesimal behavior of the Hilbert scheme of paracanonical divisors along the canonical linear series, can be used to generate inequalities among numerical invariants of X." @default.
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- W2041403874 date "2010-08-10" @default.
- W2041403874 modified "2023-10-14" @default.
- W2041403874 title "Derivative complex, BGG correspondence, and numerical inequalities for compact Kähler manifolds" @default.
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- W2041403874 doi "https://doi.org/10.1007/s00222-010-0269-4" @default.
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