Moduli of parabolic connections on curves and the Riemann-Hilbert correspondence

DOI10.1090/S1056-3911-2013-00621-9zbMath1314.14063arXivmath/0602004MaRDI QIDQ2841802

Michi-aki Inaba

Publication date: 30 July 2013

Published in: Journal of Algebraic Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0602004

Mathematics Subject Classification ID

Structure of families (Picard-Lefschetz, monodromy, etc.) (14D05) Vector bundles on curves and their moduli (14H60)

Related Items (23)

The moduli spaces of parabolic connections with a quadratic differential and isomonodromic deformations ⋮ Symplectic Resolutions for Multiplicative Quiver Varieties and Character Varieties for Punctured Surfaces ⋮ Hamiltonian structures of isomonodromic deformations on moduli spaces of parabolic connections ⋮ Isomonodromy for the degenerate fifth Painlevé equation ⋮ Line bundles on the moduli space of parabolic connections over a compact Riemann surface ⋮ On the moduli of logarithmic connections on elliptic curves ⋮ The space of monodromy data for the Jimbo-Sakai family of \(q\)-difference equations ⋮ Moduli space of factorized ramified connections and generalized isomonodromic deformation ⋮ Intersection cohomology of character varieties for punctured Riemann surfaces ⋮ The monodromy map from differential systems to the character variety is generically immersive ⋮ Geometry of the logarithmic Hodge moduli space ⋮ Parabolic opers and differential operators ⋮ MIXED HODGE STRUCTURES OF THE MODULI SPACES OF PARABOLIC CONNECTIONS ⋮ A map between moduli spaces of connections ⋮ The locus of the representation of logarithmic connections by Fuchsian equations ⋮ A relation between the parabolic Chern characters of the de Rham bundles ⋮ Flat parabolic vector bundles on elliptic curves ⋮ BPS states, torus links and wild character varieties ⋮ Explicit description of jumping phenomena on moduli spaces of parabolic connections and Hilbert schemes of points on surfaces ⋮ On the moduli spaces of framed logarithmic connections on a Riemann surface ⋮ Automorphism group of the moduli space of parabolic bundles over a curve ⋮ Unfolding of the unramified irregular singular generalized isomonodromic deformation ⋮ Moduli space of irregular rank two parabolic bundles over the Riemann sphere and its compactification

Cites Work

• Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. III
• Moduli of stable parabolic connections, Riemann-Hilbert correspondence and geometry of Painlevé equation of type VI. I
• Fuchsian moduli on a Riemann surface --- Its Poisson structure and Poincaré-Lefschetz duality
• Moduli of representations of the fundamental group of a smooth projective variety. I
• Isomorphisms between moduli spaces of \(SL(2)\)-bundles with connections on \(\mathbb{P}^1\backslash \{x_1,\dots,x_4\}\)
• Moduli of representations of the fundamental group of a smooth projective variety. II
• Equations différentielles à points singuliers réguliers
• Moduli of Semistable Logarithmic Connections
• Orthogonality of natural sheaves on moduli stacks of SL(2)-bundles with connections on \(\mathbb P^ 1\) minus 4 points.
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