Admissible Homomorphisms and Equivariant Relations Between Weighted Projective Lines

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