Maximal rank conjecture

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

Its first proof was published by Eric Larson on 14 November 2017 whilst a graduate student at MIT.

References

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