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- Title
Regularity and Multisecant Lines of Finite Schemes.
- Authors
Lee, Wanseok; Park, Euisung; Woo, Youngho
- Abstract
For a nondegenerate finite subscheme |$\Gamma$| in |${\mathbb P}^c$|, let |${\rm reg}(\Gamma)$| and |$\ell (\Gamma)$| be, respectively, the regularity of |$\Gamma$| and the largest integer |$\ell$| such that there exists an |$\ell$| -secant line to |$\Gamma$|. It is always true that |${\rm reg}(\Gamma) \geq \ell (\Gamma)$|. In this article, we show that if |${\rm reg}(\Gamma) \geq \frac{d-c+5}{2}$| then |${\rm reg}(\Gamma)$| is equal to |$\ell (\Gamma)$|. In addition, we describe the minimal free resolution of the homogeneous ideal of |$\Gamma$| for the case |${\rm reg}(\Gamma) \geq \frac{d-c+5}{2}$|.
- Subjects
MODULAR arithmetic; INTEGERS; HOMOGENEOUS spaces; MATHEMATICAL analysis; ALGEBRA
- Publication
IMRN: International Mathematics Research Notices, 2019, Vol 2019, Issue 6, p1725
- ISSN
1073-7928
- Publication type
Article
- DOI
10.1093/imrn/rnx183