The continuation method and the real analyticity of the accessory parameters: the general elliptic case

Abstract

We apply the Le Roy-Poincaré continuation method to prove the real analytic dependence of the accessory parameters on the position of the sources in Liouville theory in presence of any number of elliptic sources. The treatment is easily extended to the case of the torus with any number of elliptic singularities. A discussion is given of the extension of the method to parabolic singularities and higher genus surfaces.

28 pages, LaTeX, typos corrected

References in corpus (4)

• Classical conformal blocks
• On the solution of Liouville equation
• Torus classical conformal blocks
• Real analyticity of accessory parameters

Cited by in corpus (1)

• The continuation method and the real analyticity of the accessory parameters: the parabolic case