In this paper we study short exact sequences $ 0→P →N →I_D(k)→0 with P ,N torsion–free sheaves and D closed projective scheme. This is a classical way to construct and study projective schemes. In particular, we give homological conditions on P and N that force D to be ACM, without constrains on its codimension. As last result, we prove that if N is a higher syzygy sheaf of an ACM scheme X, the scheme D we get contains X.
Torsion-free sheaves and AMC schemes
R. Notari;
2024-01-01
Abstract
In this paper we study short exact sequences $ 0→P →N →I_D(k)→0 with P ,N torsion–free sheaves and D closed projective scheme. This is a classical way to construct and study projective schemes. In particular, we give homological conditions on P and N that force D to be ACM, without constrains on its codimension. As last result, we prove that if N is a higher syzygy sheaf of an ACM scheme X, the scheme D we get contains X.File in questo prodotto:
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