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.


The main result in this paper is about infinitesimal behavior. It would be very interesting to know whether it can be integrated to some local or even global behavior.

Dr. Lorenzo Ruffoni
Tufts University

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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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