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http://dx.doi.org/10.4134/BKMS.b150890

ON THE MINIMAL FREE RESOLUTION OF CURVES OF MAXIMAL REGULARITY

Lee, Wanseok (Department of Applied Mathematics Pukyong National University)
Park, Euisung (Department of Mathematics Korea University)

Publication Information

Bulletin of the Korean Mathematical Society / v.53, no.6, 2016 , pp. 1707-1714 More about this Journal

Abstract

Let $C{\subset}{\mathbb{P}}^r$ be a nondegenerate projective curve of degree d > r + 1 and of maximal regularity. Such curves are always contained in the threefold scroll S(0, 0, r - 2). Also some of such curves are even contained in a rational normal surface scroll. In this paper we study the minimal free resolution of the homogeneous coordinate ring of C in the case where $d{\leq}2r-2$ and C is contained in a rational normal surface scroll. Our main result provides all the graded Betti numbers of C explicitly.

Keywords

curve of maximal regularity; minimal free resolution;

Citations & Related Records

Reference

1	M. Brodmann and P. Schenzel, On projective curves of maximal regularity, Math. Z. 244 (2003), no. 2, 271-289. DOI
2	M. Brodmann and P. Schenzel, Projective curves with maximal regularity and applications to syzygies and surfaces, Manuscripta Math. 135 (2011), no. 3-4, 469-495. DOI
3	D. Eisenbud, The Geometry of syzygies, Graduate Texts in Mathematics, 229. Springer-Verlag, New York, 2005.
4	R. Ferraro, Weil divisors on rational normal scrolls, Geometric and combinatorial aspects of commutative algebra (Messina, 1999), 183-197, Lecture Notes in Pure and Appl. Math., 217, Dekker, New York, 2001.
5	L. Gruson, R. Lazarsfeld, and C. Peskine, On a theorem of Castelnuovo, and the equations defining space curves, Invent. Math. 72 (1983), no. 3, 491-506. DOI
6	U. Nagel, Arithmetically Buchsbaum divisors on varieties of minimal degree, Trans. Amer. Math. Soc. 351 (1999), no. 11, 4381-4409. DOI
7	E. Park, On syzygies of divisors on rational normal scrolls, Math. Nachr. 287 (2014), no. 11-12, 1383-1393. DOI
8	M. Green, Koszul cohomology and the geometry of projective varieties, J. Differential Geom. 19 (1984), no. 1, 125-171. DOI