Pure and Applied Mathematics Quarterly
Volume 16 (2020)
Special Issue: In Honor of Eduard Looijenga, Part 3 of 3
Isomonodromic deformations of logarithmic connections and stable parabolic vector bundles
Pages: 191 – 227
We consider irreducible logarithmic connections $(E, \delta)$ over compact Riemann surfaces $X$ of genus at least two. The underlying vector bundle $E$ inherits a natural parabolic structure over the singular locus of the connection $\delta$; the parabolic structure is given by the residues of $\delta$. We prove that for the universal isomonodromic deformation of the triple $(X, E, \delta)$, the parabolic vector bundle corresponding to a generic parameter in the Teichmüller space is parabolically stable. In the case of parabolic vector bundles of rank two, the general parabolic vector bundle is even parabolically very stable.
logarithmic connection, isomonodromic deformation, parabolic bundle, stability, very stability, Teichmüller space
2010 Mathematics Subject Classification
32G08, 14H60, 34M56, 53B05
The first author is supported by a J. C. Bose Fellowship. The second author is supported by ANR-16-CE40-0008.
Received 22 February 2019
Published 20 March 2020