A simple proof of Tyurin's babylonian tower theorem

Details A simple proof of Tyurin's babylonian tower theorem A simple proof of Tyurin's babylonian tower theorem

2010-11-03

arxiv.org/abs/1011.0870v1

Mathematics

Algebraic Geometry

Scientific paper

Using the method of Coand\u{a} 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 $P^n$ 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 $P^n$. 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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