dc.contributor.author Burban, Igor dc.contributor.author Drozd, Jurij A. dc.date.accessioned 2009-03-20T12:00:35Z dc.date.accessioned 2016-10-05T14:14:11Z dc.date.available 2009-03-20T12:00:35Z dc.date.available 2016-10-05T14:14:11Z dc.date.issued 2009-03-08 dc.identifier.uri http://publications.mfo.de/handle/mfo/1148 dc.description Research in Pairs 2009 en_US dc.description.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 $zy^2=x^3+x^2z$. en_US dc.language.iso en en_US dc.publisher Mathematisches Forschungsinstitut Oberwolfach en_US dc.relation.ispartofseries Oberwolfach Preprints;2009,14 dc.title Tilting on non-commutative rational projective curves en_US dc.type Preprint en_US dc.identifier.doi 10.14760/OWP-2009-14 local.scientificprogram Research in Pairs 2009 local.series.id OWP-2009-14 local.subject.msc 14 local.subject.msc 16
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