The locus of the representation of logarithmic connections by Fuchsian\n equations

2019/03/08 by Péter Ivanics, Ivanics, Péter
Mathematics · #14H60 #34M03 #34M35 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic and geometric function theory #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1903.03555

openalex publication_date 2019/03/08 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28

Abstract

The generic element of the moduli space of logarithmic connections with\nparabolic points on holomorphic vector bundle over the Riemann sphere can be\nrepresented by a Fuchsian equation with some singularities and some apparent\nsingularities. We analyze the case of rank 3 vector bundle which leads to\nthird order Fuchsian equation. We find coordinates on an open subset of the\nmoduli space and we construct a non-trivial part of the moduli space by blowing\nup along a variety in a special case.\n

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