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http://dx.doi.org/10.7858/eamj.2022.022

ON THE EQUATIONS DEFINING SOME CURVES OF MAXIMAL REGULARITY IN ℙ5  

Lee, Wanseok (Pukyong National University, Department of applied Mathematics)
Yang, Shuailing (Pukyong National University, Department of applied Mathematics)
Publication Information
East Asian mathematical journal / v.38, no.3, 2022 , pp. 347-355 More about this Journal
Abstract
For a nondegenerate projective variety, it is a classical problem to study its defining equations with respect to a given embedding. In this paper, we precisely determine minimal sets of generators of the defining ideals of some curves of maximal regularity in ℙ5.
Keywords
Castelnuovo-Mumford Regularity; rational normal surface scroll; rational curve; minimal generator;
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1 W. Lee and E. Park, On non-normal del Pezzo varieties. J. Algebra 387 (2013), 1128.
2 W. Lee and E. Park, On curves lying on a rational normal surface scroll. J. Pure Appl. Algebra 223 (2019), no. 10, 44584476.
3 W. Lee and W. Jang, On the equations defining some curves of maximal regualrity in ℙ4. East Asian Math. J. 35 (2019), no.1, 51-58.   DOI
4 E. Park, Projective curves of degree = codimension + 2. Math. Z. 256 (2007), no.3, 685-697.   DOI
5 Z. Fyodor, Determinants of projective varieties and their degrees. Algebraic transformation groups and algebraic varieties, 207-238, Encyclopaedia Math. Sci., 132, Springer, Berlin, 2004.   DOI
6 W. Lee, E. Park and P. Schenzel, On the classification of non-normal cubic hypersurfaces. J. Pure Appl. Algebra 215 (2011), 2034-2042.   DOI
7 W. Lee, E. Park and P. Schenzel, On the classification of non-normal complete intersection of two quadrics. J. Pure Appl. Algebra 216 (2012), no. 5, 1222-1234.   DOI
8 W. Lee and S. Yang, Defining equations of rational curves in a smooth quadric surface. East Asian Math. J. 34 (2018), no.1, 19-26
9 D. Mumford, Lectures on curves on an algebraic surface. With a section by G. M. Bergman. Annals of Mathematics Studies, No. 59 Princeton University Press, Princeton, N.J. 1966 xi+200 pp.
10 B. Saint-Donat, Sur les equations definisant une courbe algebrique, C.R. Acad. Sci. Paris, Ser. A 274 (1972), 324-327.
11 L. Gruson, R. Lazarsfeld and C. Peskine, On a theorem of Castelnovo, and the equations defining space curves , Invent. Math. 72 (1983), 491-506.   DOI
12 D. Eisenbud, J. Koh, and M. Stillman, Determinantal equations for curves of high degree, Amer. J. Math. 110 (1988), 513-539.   DOI
13 M. Decker, G.M. Greuel and H. Schonemann, Singular 3 - 1 - 2 - A computer algebra system for polynomial computations. http://www.singular.uni-kl.de (2011).
14 T. Fujita, Defining equations for certain types of polarized varieties, Complex analysis and algebraic geometry, Iwanami Shoten, Tokyo (1977), 165-173.
15 M. L. Green, Quadrics of rank four in the ideal of a canonical curve, Invent. Math. 75 (1984), no. 1, 85-104.   DOI
16 M. L. Green and R. Lazarsfeld, Some results on the syzygies of finite sets and algebraic curves, Compositio Math., 67 (1988), 301-314.
17 J. Harris, Algebraic geometry. A First course. Corrected reprint of the 1992 original. Graduate Texts in Mathematics, 133. Springer-Verlag, New York, 1995. xx+328 pp. ISBN: 0-387-97716-3 14-01