Classification of tilting bundles over a weighted projective line of type (2, 3, 3) (Q493373)
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scientific article; zbMATH DE number 6478251
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English | Classification of tilting bundles over a weighted projective line of type (2, 3, 3) |
scientific article; zbMATH DE number 6478251 |
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Classification of tilting bundles over a weighted projective line of type (2, 3, 3) (English)
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3 September 2015
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Weighted projective lines were introduced by \textit{W. Geigle} and \textit{H. Lenzing} [Lect. Notes Math. 1273, 265--297 (1987; Zbl 0651.14006)] to provide a geometric model for representations of canonical algebras in the sense of \textit{C. M. Ringel} [Tame algebras and integral quadratic forms. Lecture Notes in Mathematics. 1099. Berlin etc.: Springer-Verlag. (1984; Zbl 0546.16013)]. More precisely, they constructed tilting bundles making the category of coherent sheaves on weighted projective lines derived equivalent to representation categories of canonical algebras. \newline Following work of \textit{J. Chen} et al. [J. Pure Appl. Algebra 219, No. 7, 2538--2558 (2015; Zbl 1309.14015)] where all tilting bundles on weighted projective lines of type \((2,2,n)\) were classified in parallel to Happel and Vossieck's classification of tame concealed algebras of type \(\tilde{\mathbb{D}}_n\) [\textit{D. Happel} and \textit{D. Vossieck}, Manuscr. Math. 42, 221--243 (1983; Zbl 0516.16023)], the article under review studies the same question for the weighted projective line of type \((2,3,3)\) (i.e. tame concealed algebras of type \(\tilde{\mathbb{E}}_6\)).
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tilting bundle
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tame concealed algebra
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weighted projective line
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vector bundle
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