Abstract
Using the method of Coandă and Trautmann [Citation4], we give a simple proof of a theorem due, in the smooth case, to Tyurin [Citation9]: if a vector bundle E on a c-codimensional locally Cohen–Macaulay closed subscheme X of 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.
2010 Mathematics Subject Classification:
Notes
Communicated by L. Ein.