Tilting on non-commutative rational projective curves
Tilting on non-commutative rational projective curves
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DOI：
10.1007/s00208-010-0585-4
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发表时间：
2009-05
影响因子：
1.4
通讯作者：
I. Burban;Y. Drozd
中科院分区：
文献类型：
--
作者：
I. Burban;Y. Drozd
在本文中，我们介绍了一类新的非交换射影曲线，并表明在某些情况下，它们上的相干滑轮的派生类别具有倾斜复形。特别是，我们证明了仅以节点和尖点作为奇点的简化有理射影曲线上相干滑轮的右有界导出范畴可以完全忠实地嵌入到全局维度二的某个有限维代数的有限维表示的右有界导出范畴中。作为我们方法的应用，我们证明只有节点或尖端奇点的有理射影曲线上相干滑轮的有界派生类别的维数最多为二。在射影线的小平环的情况下，相应的倾斜代数属于众所周知的温和代数类。我们详细计算了Weierstrass节点曲线zy2=x3+x2z情况下的倾斜等价。
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 curvezy2=x3+x2z.