Kuranishi Spaces of Meromorphic Connections
Francois-Xavier Machu

TL;DR
This paper constructs Kuranishi spaces for various classes of meromorphic connections with fixed poles, providing a deformation-theoretic framework using hypercohomology and obstruction maps.
Contribution
It introduces a unified approach to deformation spaces of meromorphic connections, including integrable and logarithmic types, with explicit tangent and obstruction space descriptions.
Findings
Constructed Kuranishi spaces for all connections with fixed divisor D
Defined tangent and obstruction spaces via hypercohomology
Established the Kuranishi space as a fiber of the obstruction map
Abstract
We construct the Kuranishi spaces, or in other words, the versal deformations, for the following classes of connections with fixed divisor of poles : all such connections, as well as for its subclasses of integrable, integrable logarithmic and integrable logarithmic connections with a parabolic structure over . 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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