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• W2963995171 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 2 = x 3 + x 2 z." @default.
• W2963995171 created "2019-07-30" @default.
• W2963995171 creator A5024564994 @default.
• W2963995171 creator A5065523167 @default.
• W2963995171 date "2010-10-07" @default.
• W2963995171 modified "2023-10-14" @default.
• W2963995171 title "Tilting on non-commutative rational projective curves" @default.
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• W2963995171 doi "https://doi.org/10.1007/s00208-010-0585-4" @default.
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