Λ-modules and holomorphic Lie algebroid connections

• Autorzy: Pietro Tortella
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Holomorphic Lie algebroids; Filtered algebras; Universal enveloping algebra; Lie algebroid connections; Moduli spaces of flat connections; Generalized holomorphic bundles

Kategorie tematyczne

• 16S30: Universal enveloping algebras of Lie algebras \SeeMainly{}
• 14D20: Algebraic moduli problems, moduli of vector bundles

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2012
• Tom: 10
• Numer: 4
• Strony: 1422-1441

Daty

wydano

2012-08-01

online

2012-05-31

Twórcy

autor

Pietro Tortella

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-012-0065-z