On syzygies of linear sections
HTML articles powered by AMS MathViewer
- by Euisung Park PDF
- 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.References
- David Eisenbud, The geometry of syzygies, Graduate Texts in Mathematics, vol. 229, Springer-Verlag, New York, 2005. A second course in commutative algebra and algebraic geometry. MR 2103875
- David Eisenbud, Mark Green, Klaus Hulek, and Sorin Popescu, Restricting linear syzygies: algebra and geometry, Compos. Math. 141 (2005), no. 6, 1460–1478. MR 2188445, DOI 10.1112/S0010437X05001776
- M. Green and R. Lazarsfeld, Some results on the syzygies of finite sets and algebraic curves, Compositio Math. 67 (1988), no. 3, 301–314. MR 959214
- Robert Lazarsfeld, Positivity in algebraic geometry. I, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], vol. 48, Springer-Verlag, Berlin, 2004. Classical setting: line bundles and linear series. MR 2095471, DOI 10.1007/978-3-642-18808-4
- Uwe Nagel and Yves Pitteloud, On graded Betti numbers and geometrical properties of projective varieties, Manuscripta Math. 84 (1994), no. 3-4, 291–314. MR 1291122, DOI 10.1007/BF02567458
- Euisung Park, Higher syzygies of hyperelliptic curves, J. Pure Appl. Algebra 214 (2010), no. 2, 101–111. MR 2559684, DOI 10.1016/j.jpaa.2009.04.006
Additional Information
- Euisung Park
- Affiliation: Department of Mathematics, Korea University, Seoul 136-701, Republic of Korea
- Email: euisungpark@korea.ac.kr
- 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
- © Copyright 2015 American Mathematical Society
- 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
- MathSciNet review: 3314094