On syzygies of linear sections

Park, Euisung

doi:10.1090/S0002-9939-2015-12130-2

On syzygies of linear sections
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Proc. Amer. Math. Soc. 143 (2015), 1831-1836 Request permission

Abstract:

In this paper, we study how the minimal free resolution of a closed subscheme $X \subset \mathbb {P}^r$ relates to that of a linear section $X \cap \Lambda \subset \Lambda = \mathbb {P}^s$ $(0 < s <r)$. Our main result implies that the shape of the final non-zero row of the Betti diagram of $X$ is preserved under taking the zero-dimensional and one-dimensional linear sections.

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