The resultant on compact Riemann surfaces

Details The resultant on compact Riemann surfaces The resultant on compact Riemann surfaces

2007-10-11

arxiv.org/abs/0710.2326v2

Comm. Math. Phys., 286(2009), no 1, 313-358

Mathematics

Algebraic Geometry

44 pages

Scientific paper

10.1007/s00220-008-0622-2

We introduce a notion of resultant of two meromorphic functions on a compact Riemann surface and demonstrate its usefulness in several respects. For example, we exhibit several integral formulas for the resultant, relate it to potential theory and give explicit formulas for the algebraic dependence between two meromorphic functions on a compact Riemann surface. As a particular application, the exponential transform of a quadrature domain in the complex plane is expressed in terms of the resultant of two meromorphic functions on the Schottky double of the domain.

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