Illinois Journal of Mathematics

Kuranishi spaces of meromorphic connections

Francois-Xavier Machu

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Abstract

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.

Article information

Source
Illinois J. Math., Volume 55, Number 2 (2011), 509-541.

Dates
First available in Project Euclid: 1 February 2013

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1359762400

Digital Object Identifier
doi:10.1215/ijm/1359762400

Mathematical Reviews number (MathSciNet)
MR3020694

Zentralblatt MATH identifier
1279.14007

Subjects
Primary: 14B12: Local deformation theory, Artin approximation, etc. [See also 13B40, 13D10] 14F05: Sheaves, derived categories of sheaves and related constructions [See also 14H60, 14J60, 18F20, 32Lxx, 46M20] 14F40: de Rham cohomology [See also 14C30, 32C35, 32L10] 14H60: Vector bundles on curves and their moduli [See also 14D20, 14F05] 32G08: Deformations of fiber bundles

Citation

Machu, Francois-Xavier. Kuranishi spaces of meromorphic connections. Illinois J. Math. 55 (2011), no. 2, 509--541. doi:10.1215/ijm/1359762400. https://projecteuclid.org/euclid.ijm/1359762400


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