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- Title
Tilting on non-commutative rational projective curves.
- Authors
Burban, Igor; Drozd, Yuriy
- Abstract
In this article we introduce a new class of non-commutative projective curves and show that in certain cases the derived category of coherent sheaves on them has a tilting complex. In particular, we prove that the right bounded derived category of coherent sheaves on a reduced rational projective curve with only nodes and cusps as singularities, can be fully faithfully embedded into the right bounded derived category of the finite dimensional representations of a certain finite dimensional algebra of global dimension two. As an application of our approach we show that the dimension of the bounded derived category of coherent sheaves on a rational projective curve with only nodal or cuspidal singularities is at most two. In the case of the Kodaira cycles of projective lines, the corresponding tilted algebras belong to a well-known class of gentle algebras. We work out in details the tilting equivalence in the case of the Weierstrass nodal curve zy = x + x z.
- Subjects
CURVES; ALGEBRA; MATHEMATICAL analysis; GEOMETRY; MATHEMATICAL singularities
- Publication
Mathematische Annalen, 2011, Vol 351, Issue 3, p665
- ISSN
0025-5831
- Publication type
Article
- DOI
10.1007/s00208-010-0585-4