Rigidity of moduli spaces and algebro-geometric constructions

TL;DR

This paper introduces principles and conjectures about the rigidity of moduli spaces in algebraic geometry, linking geometric, topological, and group-theoretic aspects, some of which are already proved.

Contribution

It proposes guiding principles that lead to new conjectures on the rigidity of moduli spaces, connecting algebraic geometry with group theory and topology.

Findings

Some conjectures have been proved.

Guiding principles suggest further research directions.

Connections between rigidity and various mathematical areas.

Abstract

In this paper we propose two guiding principles that suggest a number of conjectures (some now proved) about various forms of rigidity for moduli spaces arising in algebraic geometry. Such conjectures have group-theoretic, topological and holomorphic aspects, and so they also provide motivation for natural problems in geometric group theory and topology.