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Λ-modules and holomorphic Lie algebroid connections

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Tortella P.

Open Mathematics

2012

tom 10

nr 4

1422-1441

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 $ \equiv :Gr\Lambda \to Sym \bullet _{\mathcal{O}_X } \mathcal{G}$ is an isomorphism, and pairs (L, Σ), where L is a holomorphic Lie algebroid structure on $\mathcal{G}$ 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.

Ograniczanie wyników

1 Open Mathematics

1 Tortella P.

1 2012

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Λ-modules and holomorphic Lie algebroid connections