A simple proof of Tyurin's babylonian tower theorem

2010/11/03 by Iustin Coandă, Coanda, Iustin
Mathematics · #14B10 #14F05 #14J60 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1011.0870

openalex publication_date 2010/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using the method of Coandă and Trautmann (2006), we give a simple proof of the following theorem due to Tyurin (1976) in the smooth case: if a vector bundle E on a c-codimensional locally Cohen-Macaulay closed subscheme X of the projective space Pⁿ extends to a vector bundle F on a similar closed subscheme Y of P^N, for every N > n, then E is the restriction to X of a direct sum of line bundles on Pⁿ. 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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