Draft:Maximal rank conjecture

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{{AFC comment|1=Needs discussion outside Eric Larson's works. Ca ^{talk to me!} 13:10, 1 December 2024 (UTC)}}

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In algebraic geometry,

Let $C \subset$ $\mathbb{P}^r$ 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 $H^0(\mathcal{O}_{\mathbb{P}^r}(m)) \to H^0(\mathcal{O}_{\mathbb{C}}(m))$ are of maximal rank; this determines the Hilbert function of $C$ .{{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 }}

Its first proof was published by Eric Larson on 14 Nov 2017{{Citation |last=Larson|first=Eric |title=The Maximal Rank Conjecture |date=2018-09-18 |arxiv=1711.04906}} whilst a graduate student at MIT.{{Cite web |date=2022-08-25 |title=Old Problem About Algebraic Curves Falls to Young Mathematicians |url=https://www.quantamagazine.org/old-problem-about-algebraic-curves-falls-to-young-mathematicians-20220825/ |access-date=2025-03-07 |website=Quanta Magazine |language=en}}

References

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:Category:Conjectures

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