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Let $C \subset \P^r$ 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.
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참고문헌 (8)
참고문헌 신청
M. Brodmann / 2003 / On projective curves of maximal regularity / Math. Z 244(2):271~289
M. Brodmann / 2011 / Projective curves with maximal regularity and applications to syzygies and surfaces / Manuscripta Math 135(3-4):469~495
D. Eisenbud / 2005 / The Geometry of syzygies / Springer-Verlag
R. Ferraro / 2001 / Geometric and combinatorial aspects of commutative algebra / Dekker :183~197
M. Green / 1984 / Koszul cohomology and the geometry of projective varieties / J. Differential Geom 19(1):125~171
M. Brodmann / 2011 / Projective curves with maximal regularity and applications to syzygies and surfaces / Manuscripta Math 135(3-4):469~495
D. Eisenbud / 2005 / The Geometry of syzygies / Springer-Verlag
R. Ferraro / 2001 / Geometric and combinatorial aspects of commutative algebra / Dekker :183~197
M. Green / 1984 / Koszul cohomology and the geometry of projective varieties / J. Differential Geom 19(1):125~171
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