ar X iv : m at h / 05 07 16 2 v 1 [ m at h . A G ] 7 J ul 2 00 5 A SPECIALITY THEOREM FOR CURVES IN P 5
نویسندگان
چکیده
Let C ⊂ P be an integral projective curve. One defines the speciality index e(C) of C as the maximal integer t such that h(C, ωC(−t)) > 0, where ωC denotes the dualizing sheaf of C. Extending a classical result of Halphen concerning the speciality of a space curve, in the present paper we prove that if C ⊂ P is an integral degree d curve not contained in any surface of degree < s, in any threefold of degree < t, and in any fourfold of degree < u, and if d >> s >> t >> u ≥ 1, then e(C) ≤ d s + s t + t u +u− 6. Moreover equality holds if and only if C is a complete intersection of hypersurfaces of degrees u, t u , s t and d s . We give also some partial results in the general case C ⊂ P, r ≥ 3.
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