Draft:Maximal rank conjecture

Submission declined on 1 December 2024 by Ca (talk).

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Declined by Ca 3 days ago. Last edited by Ca 3 days ago. Reviewer: Inform author.

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

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 $C$ .^[1]

Its first proof was published by Eric Larson on 14 Nov 2017.^[2]

References

^ Larson, Eric (1 August 2020). "The Maximal Rank Conjecture for sections of curves". Journal of Algebra. 555: 223–245. arXiv:1208.2730. doi:10.1016/j.jalgebra.2020.03.006. ISSN 0021-8693.
^ Larson, Eric (18 September 2018), The Maximal Rank Conjecture, arXiv:1711.04906

[1] Larson, Eric (1 August 2020). "The Maximal Rank Conjecture for sections of curves". Journal of Algebra. 555: 223–245. arXiv:1208.2730. doi:10.1016/j.jalgebra.2020.03.006. ISSN 0021-8693.

[2] Larson, Eric (18 September 2018), The Maximal Rank Conjecture, arXiv:1711.04906

[1]

[2]