Families of Riemann surfaces over the punctured disk

Clifford John Earle, Jr. and Patricia Lilaine Sipe

Vol. 150 (1991), No. 1, 79–96

DOI: 10.2140/pjm.1991.150.79

Abstract

We study holomorphic families of compact Riemann surfaces over the punctured unit disk. For every genus p ≥ 3 we define a family whose relative canonical bundle has no roots of order n > 2. The monodromy group of that family is generated by a product of powers of commuting Dehn twists. We give necessary and sufficient conditions for such a product to generate the monodromy group of a family over the punctured disk.

Mathematical Subject Classification 2000

Primary: 30F60

Secondary: 32G15

Milestones

Received: 13 December 1988

Revised: 14 August 1990

Published: 1 September 1991