Paper
A Non-Abelian Approach to Riemann Surfaces
Authors
Mehrzad Ajoodanian
Abstract
We develop a non-abelian, gauge-theoretic framework for the Schwarzian derivative and for second-order differential equations on Riemann surfaces. As applications, we extend Dedekind's Schwarzian approach to elliptic periods to generic one-parameter families of curves of genus $g$ by replacing the non-canonical scalar Picard--Fuchs equation of order $2g$ with a canonical second-order equation with $g\times g$ matrix coefficients on the Hodge bundle. In higher dimensions, we discuss periods of a one-parameter family of cubic threefolds via the intermediate Jacobian. Finally, we discuss mass--spring systems in mechanics as a natural testing ground for the non-abelian Schwarzian viewpoint.
Metadata
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Raw Data (Debug)
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