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- W3015125978 abstract "Let C⊂Pr be a general curve of genus g embedded via a general linear series of degree d. The Maximal Rank Conjecture asserts that the restriction maps H0(OPr(m))→H0(OC(m)) are of maximal rank; this determines the Hilbert function of C. In this paper, we prove an analogous statement for the union of hyperplane sections of general curves. More specifically, if H⊂Pr is a general hyperplane, and C1,C2,…,Cn are general curves, we show H0(OH(m))→H0(O(C1∪C2∪⋯∪Cn)∩H(m)) is of maximal rank, except for some counterexamples when m=2. As explained in [5], this result plays a key role in the author's proof of the Maximal Rank Conjecture [7]." @default.
- W3015125978 created "2020-04-10" @default.
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- W3015125978 date "2020-08-01" @default.
- W3015125978 modified "2023-09-25" @default.
- W3015125978 title "The Maximal Rank Conjecture for sections of curves" @default.
- W3015125978 cites W1839261942 @default.
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- W3015125978 doi "https://doi.org/10.1016/j.jalgebra.2020.03.006" @default.
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