The thesis is concerned with the construction and the study of moduli spaces of holomorphic Lie algebroid connections. It provides a classification of sheaves of almost polynomial filtered algebras on a smooth projective complex variety in terms of holomorphic Lie algebroids and their cohomology classes. This permits to build moduli spaces of holomorphic Lie agebroid connections via Simpson’s formalism of Lambda-modules. Furthermore, the deformation theory of such connections is studied, and the germ of their moduli spaces in the rank two case is computed when the base variety is a curve.

Lambda-modules and holomorphic Lie algebroids / Tortella, Pietro. - (2011 Oct 06).

Lambda-modules and holomorphic Lie algebroids

Tortella, Pietro
2011-10-06

Abstract

The thesis is concerned with the construction and the study of moduli spaces of holomorphic Lie algebroid connections. It provides a classification of sheaves of almost polynomial filtered algebras on a smooth projective complex variety in terms of holomorphic Lie algebroids and their cohomology classes. This permits to build moduli spaces of holomorphic Lie agebroid connections via Simpson’s formalism of Lambda-modules. Furthermore, the deformation theory of such connections is studied, and the germ of their moduli spaces in the rank two case is computed when the base variety is a curve.
Bruzzo, Ugo
Markushevich, Dimitri
Tortella, Pietro
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11767/4665
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