Pullback Moduli Spaces

Abstract

Geometric invariant theory can be used to construct moduli spaces associated to representations of finite dimensional algebras. One difficulty which occurs in various natural cases is that nonisomorphic modules are sent to the same point in the moduli spaces which arise. In this article, we study how this collapsing phenomenon can sometimes be reduced by considering pullbacks of modules for an auxiliary algebra. One application is a geometric proof that the twisting action of an algebra automorphism induces an algebraic isomorphism between moduli spaces.

Key Words:

• Algebra automorphisms
• Moduli spaces
• Pullbacks
• Representations of finite dimensional algebras

2000 Mathematics Subject Classification:

• Primary 16G10
• Secondary 14D22, 16W20

ACKNOWLEDGMENT

The first author was supported in part by NSF Grants DMS01-39737, DMS06-51332, and NSA Grant H98230-06-1-0021. The second author was supported in part by NSF Grants DMS00-70433 and DMS05-00106.

Notes

Communicated by D. Zacharia.