Schiffer variations and Abelian differentials
Geometric Topology
2015-09-15 v2
Abstract
Deformations of compact Riemann surfaces are considered using a \v{C}ech cohomology sliding overlaps approach. Cocycles are calculated for conformal cutting and regluing deformations at zeros of Abelian differentials. A second order deformation expansion is presented for the Riemann period matrix. A complete deformation expansion is presented for Abelian differentials. Schiffer's kernel function approach for deformations of a Green's function is followed.
Cite
@article{arxiv.1508.01100,
title = {Schiffer variations and Abelian differentials},
author = {Scott A. Wolpert},
journal= {arXiv preprint arXiv:1508.01100},
year = {2015}
}
Comments
26 pages, 3 figures; version 2 includes discussion of the relation to the Kontsevich-Zorich breaking up a zero deformation and of breaking up higher order zeros