Abstract
We give a complete classification of tilting sheaves over weighted projective lines of weight type (p).
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References
Assem I, Skowrónski A. Iterated tilted algebras of type Ãn. Math Z, 1987, 195(2): 269–290
Brenner S, Butler M C R. Generalizations of the Bernstein-Gelfand-Ponomarev reflection functors. In: Dlab V, Gabriel P, eds. Representation Theory, II. Lecture Notes in Math, Vol 832. Berlin: Springer, 1980, 103–169
Buan A B, Krause H. Tilting and cotilting for quivers of type Ãn. J Pure Appl Algebra, 2004, 190(1): 1–21
Chen J, Lin Y, Ruan S. Abelianness of the “missing part” from a sheaf category to a module category. Sci China Math, 2014, 57(2): 245–258
Chen J, Lin Y, Ruan S. Tilting bundles and the missing part on a weighted projective line of type (2, 2, n). J Pure Appl Algebra, 2015, 219(7): 2538–2558
Geigle W, Lenzing H. A class of weighted projective curves arising in representation theory of finite dimensional algebras. In: Greuel G-M, Trautmann, G, eds. Singularities, Representation of Algebras, and Vector Bundles. Lecture Notes in Math, Vol 1273. Berlin: Springer, 1987, 265–297
Happel D, Ringel C M. Tilted algebras. Trans Amer Math Soc, 1982, 274(2): 399–443
Hille L. Tilting Modules over the Path Algebra of Type A, Polytopes, and Catalan Numbers. ArXiv: 1505.06011
Lenzing H. Weighted projective lines and applications. In: Skowrónski A, Yamagata K, eds. Representations of Algebras and Related Topics. Zürich: European Math Soc, 2011, 153–187
Lenzing H, Meltzer H. Tilting sheaves and concealed-canonical algebras. In: Bautista R, Martínez-Villa R, de la Pe˜na J A, eds. Representation Theory of Algebras. CMS Conference Proceedings, Vol 18. Providence: Amer Math Soc, 1996, 455–473
Lin Y, Wang M. The numbers of tilting modules over path algebras of An. J Math Res Exposition, 2005, 25(1): 144–147 (in Chinese)
Meltzer H. Exceptional Vector Bundles, Tilting Sheaves and Tilting Complexes for Weighted Projective Lines. Mem Amer Math Soc, Vol 171, No 808. Providence: Amer Math Soc, 2004
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Zhang, X. Tilting sheaves for weighted projective lines of weight type (p). Front. Math. China 13, 715–724 (2018). https://doi.org/10.1007/s11464-018-0701-4
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DOI: https://doi.org/10.1007/s11464-018-0701-4