On the speciality of a curve

Rosario Strano


Let C ⊂ P rk, k algebraically closed field of characteristic 0, be a curve and let e(C)={max n | H1(OC(n))0} its speciality. Let Γ be the generic hyperplane section and ε ={max n | H 1(IΓ(n))≠0}. We prove that, if Γ is generated in degree ≤ ε , then e(C)=ε -1. In the case r=3 we discuss some relations between e(C) and the Hilbert function of Γ.

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