2017/04/19 by Dmitry Korotkin
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Function (biology) #Genus #Geometry #Gravitational singularity #Integral equation #Mathematical analysis #Mathematics #Monodromy #Pure mathematics #Riemann surface #Riemann–Stieltjes integral #Surface (topology) #hep-th #math-ph #math.MP #nlin.SI
paper · pdf · doi:10.1016/j.nuclphysb.2017.12.019
arxiv created 2017/04/19 · openalex publication_date 2017/12/27 · arxiv updated 2018/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We describe projective structures on a Riemann surface corresponding to monodromy groups which have trivial S L ( 2 ) monodromies around singularities and trivial P S L ( 2 ) monodromies along homologically non-trivial loops on a Riemann surface. We propose a natural higher genus analog of Stieltjes–Bethe equations. Links with branched projective structures and with Hurwitz spaces with ramifications of even order are established. We find a higher genus analog of the genus zero Yang–Yang function (the function generating accessory parameters) and describe its similarity and difference with Bergman tau-function on the Hurwitz spaces.