The Maximal Rank Conjecture for sections of curves

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The Maximal Rank Conjecture for Sections of Curves

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...

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The Maximal Rank Conjecture

Let C be a general curve of genus g, embedded in Pr via a general linear series of degree d. In this paper, we prove the Maximal Rank Conjecture, which determines the Hilbert function of C ⊂ Pr.

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Article history: Received 20 September 2016 Available online xxxx

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ژورنال

عنوان ژورنال: Journal of Algebra

سال: 2020

ISSN: 0021-8693

DOI: 10.1016/j.jalgebra.2020.03.006