Uniqueness of varieties of minimal degree containing a given scheme

Casanellas, M.

doi:10.1090/S0002-9947-03-03421-4

Uniqueness of varieties of minimal degree containing a given scheme
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Trans. Amer. Math. Soc. 356 (2004), 1875-1888 Request permission

Abstract:

We prove that if $X \subset \mathbb {P}^N$ has dimension $k$ and it is $r$-Buchsbaum with $r>\max {(\operatorname {codim}{X}-k,0)}$, then $X$ is contained in at most one variety of minimal degree and dimension $k+1$.

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