Admissible homomorphisms and equivariant relations between weighted projective lines

TL;DR

This paper characterizes equivariant relations between weighted projective lines induced by string group actions, showing they correspond to admissible homomorphisms, and classifies these for specific types.

Contribution

It establishes a correspondence between equivariant relations and admissible homomorphisms, providing a classification for certain weighted projective lines.

Findings

Equivariant equivalences are characterized by admissible homomorphisms.

Classification of equivariant relations for domestic and tubular types.

Provides a framework for understanding degree-shift actions on weighted projective lines.

Abstract

The string group acts on the category of coherent sheaves over a weighted projective line by degree-shift actions. We study the equivariant equivalence relations induced by degree-shift actions between weighted projective lines. We prove that such an equivariant equivalence is characterized by an admissible homomorphism between the associated string groups. We classify all these equivariant equivalences for the weighted projective lines of domestic and tubular types.