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The quaternionic Riemann -Roch theorem

Matthew Leonard Auth, University of Massachusetts Amherst


The aim is to define what it means to be a meromorphic section of a quaternionic holomorphic vector bundle over a compact Riemann surface and then prove a version of the Riemann-Rock theorem for divisors that generalizes the classical theorem. A meromorphic section of a quaternionic spin bundle provides Weierstrass data (modulo period conditions) for a conformal map into Euclidean three space with prescribed mean curvature half density.

Subject Area


Recommended Citation

Auth, Matthew Leonard, "The quaternionic Riemann -Roch theorem" (2002). Doctoral Dissertations Available from Proquest. AAI3039335.