What is it about?
Complex projective structures are a geometric tool to study the relation between algebra (group representations) and analysis (complex ODEs) on surfaces. We study how these structures can be deformed in a way that preserves both the algebraic and the analytic side.
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Why is it important?
Hilbert's XXI problem asks to determine which group representations correspond to certain classes of ODEs. In genus 2 or higher, this is still open even in the simple case of linear ODE of rank 2. Our contribution is a step forward in the solution of this case.
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This page is a summary of: Local deformations of branched projective structures: Schiffer variations and the Teichmüller map, Geometriae Dedicata, February 2021, Springer Science + Business Media, DOI: 10.1007/s10711-021-00601-6.
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