Wide subcategories of a domestic weighted projective line

Abstract

For a weighted projective line X, a wide subcategory of the category coh-X of coherent sheaves over X is called c→-invariant if it is closed under the grading shift of the canonical element c→. We proved that a c→-invariant wide subcategory of coh-X containing a vector bundle is the perpendicular category of a torsion exceptional sequence. If X is of domestic type, then the poset of wide subcategories of coh-X is the union of the poset of wide subcategories generated by an exceptional sequence and the poset of c→-invariant wide subcategories.