Slicing, skinning, and grafting

TL;DR

This paper proves that Bers slices are never algebraic and skinning maps are never constant, using grafting and complex projective structures, revealing fundamental properties of character varieties and deformation spaces.

Contribution

It establishes that Bers slices are not algebraic and skinning maps are non-constant, advancing understanding of deformation spaces in complex geometry.

Findings

Bers slices are never algebraic.

Skinning maps are never constant.

Uses grafting and complex projective structures in proofs.

Abstract

We prove that a Bers slice is never algebraic, meaning that its Zariski closure in the character variety has strictly larger dimension. A corollary is that skinning maps are never constant. The proof uses grafting and the theory of complex projective structures.