On the syzygies of quasi-complete intersection space curves
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- by Youngook Choi
- Proc. Amer. Math. Soc. 137 (2009), 3999-4006
- DOI: https://doi.org/10.1090/S0002-9939-09-09996-1
- Published electronically: July 24, 2009
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Abstract:
In this paper, we discuss minimal free resolutions of the homogeneous ideals of quasi-complete intersection space curves. We show that if $X$ is a quasi-complete intersection curve in $\mathbb P^3$, then $I_X$ has a minimal free resolution \[ 0\to \oplus _{i=1}^{\mu -3} S(d_{i+3}+c_1)\to \oplus _{i=1}^{2\mu -4}S(-e_i)\to \oplus _{i=1}^\mu S(-d_i)\to I_X\to 0, \] where $d_i,e_i\in \mathbb Z$ and $c_1=-d_1-d_2-d_3$. Therefore the ranks of the first and the second syzygy modules are determined by the number of elements in a minimal generating set of $I_X$. Also we give a relation for the degrees of syzygy modules of $I_X$. Using this theorem, one can construct a smooth quasi-complete intersection curve $X$ such that the number of minimal generators of $I_X$ is $t$ for any given positive integer $t\in \mathbb Z^+$.References
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Bibliographic Information
- Youngook Choi
- Affiliation: Department of Mathematics Education, Yeungnam University, 214-1 Daedong Gyeongsan, 712-749, Gyeongsangbuk-do, Republic of Korea
- MR Author ID: 709698
- Email: ychoi824@ynu.ac.kr
- Received by editor(s): July 1, 2008
- Received by editor(s) in revised form: April 5, 2009
- Published electronically: July 24, 2009
- Additional Notes: This work was supported by a Korea Research Foundation Grant funded by the Korean Government (MOEHRD, Basic Research Promotion Fund), KRF-2007-521-C00002.
- Communicated by: Bernd Ulrich
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 3999-4006
- MSC (2000): Primary 14M07, 14N05, 14M06
- DOI: https://doi.org/10.1090/S0002-9939-09-09996-1
- MathSciNet review: 2538560