Kuranishi Spaces of Meromorphic Connections

Details Kuranishi Spaces of Meromorphic Connections Kuranishi Spaces of Meromorphic Connections

2010-09-09

arxiv.org/abs/1009.1898v3

Mathematics

Algebraic Geometry

27 pages, one figure, Accepted in Illinois Journal of Mathematics

Scientific paper

We construct the Kuranishi spaces, or in other words, the versal deformations, for the following classes of connections with fixed divisor of poles $D$: all such connections, as well as for its subclasses of integrable, integrable logarithmic and integrable logarithmic connections with a parabolic structure over $D$ . The tangent and obstruction spaces of deformation theory are defined as the hypercohomology of an appropriate complex of sheaves, and the Kuranishi space is a fiber of the formal obstruction map.

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