The Maximal Rank Conjecture for Sections of Curves
نویسنده
چکیده
Let C ⊂ Pr be a general curve of genus g embedded via a general linear series of degree d. The well-known Maximal Rank Conjecture asserts that the restriction maps H(OPr(m)) → H(OC(m)) are of maximal rank; if known, this conjecture would determine the Hilbert function of C. In this paper, we prove an analogous statement for the hyperplane sections of general curves. More specifically, if H ⊂ Pr is a general hyperplane, we show that H(OH(m)) → H(OC∩H(m)) is of maximal rank, except for some counterexamples when m = 2. We also prove a similar theorem for the intersection of a general space curve with a quadric.
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