Indecomposable sheaves on the weighted projective line (2,2,n) are bijectively drawn as skew-curves on a symmetric cylinder, with pseudo-triangulations corresponding exactly to tilting sheaves and flips to mutations.
A note on Serre duality and equivariantization
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For an abelian category with a Serre duality and a finite group action, we compute explicitly the Serre duality on the category of equivariant objects. Special cases and examples are discussed. In particular, an abelian category with a periodic Serre duality and its equivariantization are studied.
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Geometric-combinatorial approaches to tilting theory for weighted projective lines
Indecomposable sheaves on the weighted projective line (2,2,n) are bijectively drawn as skew-curves on a symmetric cylinder, with pseudo-triangulations corresponding exactly to tilting sheaves and flips to mutations.