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Let $Y\subset \PP^3$ be a degree $d$ reduced curve with only planar singularities. We prove that $h^i(\Ii _Y(t)) =0$, $i=1,2$, for all $t\ge d-2$. We use this result and linkage to construct some triples $(d,g,s)$, $d>s^2$, with very large $g$ for which there is a smooth and connected curve of degree $d$ and genus $g$, $h^0(\Ii _C(s)) =1$ and describe the Hartshorne-Rao module of $C$.
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참고문헌 (17)
참고문헌 신청
B. Ballet / 1993 / Genre de courbes lisses tracees sur certaines surfaces rationnelles de P3 / Bull. Soc. Math. France 121(3):383~402
E. Ballico / 1986 / A program for space curves / Rend. Sem. Mat. Univ. Politec. Torino 1986(Special Issue):25~42
A. Dolcetti / 1988 / Halphen's gaps for space curves of submaximum genus / Bull. Soc. Math. France 116(2):157~170
Ph. Ellia / 1987 / Une remarque sur un theoreme de Gruson-Lazarsfeld-Peskine / Arch. Math. (Basel) 48(5):406~408
Ph. Ellia / 1989 / Sur les lacunes d'Halphen, in Algebraic curves and projective geometry (Trento, 1988), 43-65 / Lecture Notes in Math 1389:1989
E. Ballico / 1986 / A program for space curves / Rend. Sem. Mat. Univ. Politec. Torino 1986(Special Issue):25~42
A. Dolcetti / 1988 / Halphen's gaps for space curves of submaximum genus / Bull. Soc. Math. France 116(2):157~170
Ph. Ellia / 1987 / Une remarque sur un theoreme de Gruson-Lazarsfeld-Peskine / Arch. Math. (Basel) 48(5):406~408
Ph. Ellia / 1989 / Sur les lacunes d'Halphen, in Algebraic curves and projective geometry (Trento, 1988), 43-65 / Lecture Notes in Math 1389:1989
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