A Simple Proof of Tyurin's Babylonian Tower Theorem |
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Authors: | Iustin Coandă |
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Affiliation: | 1. Institute of Mathematics of the Romanian Academy , Bucharest , Romania Iustin.Coanda@imar.ro |
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Abstract: | Using the method of Coand? and Trautmann [4 Coand? , I. , Trautmann , G. ( 2006 ). The splitting criterion of Kempf and the Babylonian tower theorem . Comm. Algebra 34 : 2485 – 2488 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]], we give a simple proof of a theorem due, in the smooth case, to Tyurin [9 Tyurin , A. N. ( 1976 ). Finite dimensional vector bundles over infinite varieties . Math. USSR Izv. 10 : 1187 – 1204 .[Crossref], [Web of Science ®] , [Google Scholar]]: if a vector bundle E on a c-codimensional locally Cohen–Macaulay closed subscheme X of ? n extends to a vector bundle F on a similar closed subscheme Y of ? N , for every N > n, then E is the restriction to X of a direct sum of line bundles on ? n . Using the same method, we also provide a proof of the Babylonian tower theorem for locally complete intersection subschemes of projective spaces. |
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Keywords: | Babylonian tower Projective scheme Vector bundle |
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