Let X be a complex smooth projective variety, and G a locally free sheaf on X. We show that there is a one-to-one correspondence between pairs (Λ, Ξ), where Λ is a sheaf of almost polynomial filtered algebras over X satisfying Simpson’s axioms and is an isomorphism, and pairs (L, Σ), where L is a holomorphic Lie algebroid structure on and Σ is a class in F 1 H 2(L, ℂ), the first Hodge filtration piece of the second cohomology of L. As an application, we construct moduli spaces of semistable flat L-connections for any holomorphic Lie algebroid L. Particular examples of these are given by generalized holomorphic bundles for any generalized complex structure associated to a holomorphic Poisson manifold.
@article{bwmeta1.element.doi-10_2478_s11533-012-0065-z,
author = {Pietro Tortella},
title = {$\Lambda$-modules and holomorphic Lie algebroid connections},
journal = {Open Mathematics},
volume = {10},
year = {2012},
pages = {1422-1441},
zbl = {1279.14016},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0065-z}
}
Pietro Tortella. Λ-modules and holomorphic Lie algebroid connections. Open Mathematics, Tome 10 (2012) pp. 1422-1441. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0065-z/
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