On the middle convolution

Abstract

We present a cohomological interpretation of the middle convolution functor MC and find an explicit Riemann-Hilbert correspondence for MC_λ. This leads to an algorithm for the construction of Fuchsian systems which correspond to irreducible rigid local systems under the Riemann-Hilbert correspondence. Also, the effect of MC_λon the p-curvatures ist determined and new examples of differential systems are found which satisfy the Grothendieck-Katz p-curvature conjecture.

Cited by in corpus (8)

• The Fuchsian differential equation of the square lattice Ising model $\chi (3)$ susceptibility
• Picard-Fuchs Differential Equations for Families of K3 Surfaces
• Integral representation of solutions to Fuchsian system and Heun's equation
• Painlevé equations and the middle convolution
• Twisted Euler transform of differential equations with an irregular singular point
• Katz's middle convolution algorithm
• Variation of parabolic cohomology and Poincare duality
• Variation of local systems and parabolic cohomology