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On syzygies of linear sections


Author: Euisung Park
Journal: Proc. Amer. Math. Soc. 143 (2015), 1831-1836
MSC (2010): Primary 14N05, 13D02
DOI: https://doi.org/10.1090/S0002-9939-2015-12130-2
Published electronically: January 9, 2015
MathSciNet review: 3314094
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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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Additional Information

Euisung Park
Affiliation: Department of Mathematics, Korea University, Seoul 136-701, Republic of Korea
Email: euisungpark@korea.ac.kr

DOI: https://doi.org/10.1090/S0002-9939-2015-12130-2
Keywords: Minimal free resolution, Linear section
Received by editor(s): October 31, 2012
Received by editor(s) in revised form: January 3, 2013
Published electronically: January 9, 2015
Communicated by: Irena Peeva
Article copyright: © Copyright 2015 American Mathematical Society