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In this work we obtain conditions for nonspecial line bundles on general k-gonal curves failing to be normally generated. Let L be a nonspecial very ample line bundle on a general k-gonal curve X with k ≥ 4 and degL ≥ 3 2 g + g−2 k + 1. If L fails to be normally generated, then L is isomorphic to KX −(ng1k +B)+R for some n ≥ 1, B and R satisfying (1) h0(R) = h0(B) = 1, (2) n+3 ≤ degR ≤ 2n+2, (3) deg(R∩F) ≤ 1 for any F ∈ g1k . Its converse also holds under some additional restrictions. As a corollary, a very ample line bundle L ≃ KX−g0 d+ξ0/e is normally generated if g0/d ∈ X(d) and ξ0/e ∈ X(e) satisfy d ≤ g/2 − g−2/k − 3, supp(g0/d ∩ ξ0/e ) = ∅ and deg(g0/d ∩ F) ≤ k − 2 for any F ∈ g1/k .
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참고문헌 (8)
참고문헌 신청
A. Mattuck / 1961 / Symmetric products and Jacobians / Amer. J. Math 83 : 189 ~ 206
D. Mumford / 1969 / Varieties defined by quadratic equations, Questions on Algebraic Varieties / Edizioni Cremonese : 29 ~ 100
E. Ballico / 2003 / Normal generation of line bundles on a general k-gonal algebraic curve / Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8) 6 (3) : 557 ~ 562
G. Castelnuovo / 1893 / Sui multipli di una serie lineare di gruppi di punti appartenente ad una curva algebrica / Rend. Circ. Mat. Palermo 7 : 89 ~ 110
G. Martens / 1986 / Line bundles and syzygies of trigonal curves / Abh. Math. Sem. Univ. Hamburg 56 : 169 ~ 189
D. Mumford / 1969 / Varieties defined by quadratic equations, Questions on Algebraic Varieties / Edizioni Cremonese : 29 ~ 100
E. Ballico / 2003 / Normal generation of line bundles on a general k-gonal algebraic curve / Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8) 6 (3) : 557 ~ 562
G. Castelnuovo / 1893 / Sui multipli di una serie lineare di gruppi di punti appartenente ad una curva algebrica / Rend. Circ. Mat. Palermo 7 : 89 ~ 110
G. Martens / 1986 / Line bundles and syzygies of trigonal curves / Abh. Math. Sem. Univ. Hamburg 56 : 169 ~ 189
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