On the Rank of Quadratic Equations for Curves of High Degree
- Authors
- Park, Euisung
- Issue Date
- 12월-2022
- Publisher
- SPRINGER BASEL AG
- Keywords
- Projective curve; homogeneous ideal; property QR(3)
- Citation
- MEDITERRANEAN JOURNAL OF MATHEMATICS, v.19, no.6
- Indexed
- SCIE
SCOPUS
- Journal Title
- MEDITERRANEAN JOURNAL OF MATHEMATICS
- Volume
- 19
- Number
- 6
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/145626
- DOI
- 10.1007/s00009-022-02170-8
- ISSN
- 1660-5446
- Abstract
- Let C subset of P-r be a linearly normal curve of arithmetic genus g and degree d. In Saint-Donat (CR Acad Sci Paris Ser A 274: 324-327, 1972), B. Saint-Donat proved that the homogeneous ideal I(C) of C is generated by quadratic equations of rank at most 4 whenever d >= 2g+ 2. Also, in Eisenbud et al. (Amer J Math 110: 513-539, 1988) Eisenbud, Koh and Stillman proved that I(C) admits a determinantal presentation if d >= 4g + 2. In this paper, we will show that I(C) can be generated by quadratic equations of rank 3 if either g = 0,1 and d >= 2g + 2 or else g >= 2 and d >= 4g + 4.
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