View source for Draft:Maximal rank conjecture

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{{AFC comment|1=Needs discussion outside Eric Larson's works. [[User:Ca|Ca]] <i><sup style="display:inline-flex;rotate:7deg;">[[User talk:Ca|talk to me!]]</sup></i> 13:10, 1 December 2024 (UTC)}}

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Let  <math>C \subset</math> <math>\mathbb{P}^r</math> 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 <math>H^0(\mathcal{O}_{\mathbb{P}^r}(m)) \to H^0(\mathcal{O}_{\mathbb{C}}(m))</math> are of maximal rank; this determines the Hilbert function of ''<math>C</math>.''<ref>{{Cite journal |last=Larson |first=Eric |date=2020-08-01 |title=The Maximal Rank Conjecture for sections of curves |url=https://www.sciencedirect.com/science/article/pii/S0021869320301186 |journal=Journal of Algebra |volume=555 |pages=223–245 |doi=10.1016/j.jalgebra.2020.03.006 |issn=0021-8693|arxiv=1208.2730 }}</ref>

Its first proof was published by Eric Larson on 14 Nov 2017.<ref>{{Citation |last=Larson|first=Eric |title=The Maximal Rank Conjecture |date=2018-09-18 |arxiv=1711.04906}}</ref>

==References==
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