• Corpus ID: 5464568

The maximal rank conjecture

@article{Larson2018TheMR,
title={The maximal rank conjecture},
author={Eric Larson},
journal={arXiv: Algebraic Geometry},
year={2018}
}
• Eric Larson
• Published 14 November 2017
• Mathematics
• arXiv: Algebraic Geometry
Let C be a general curve of genus g, embedded in P^r via a general linear series of degree d. In this paper, we prove the Maximal Rank Conjecture, which determines the Hilbert function of C.
Degenerations of Curves in Projective Space and the Maximal Rank Conjecture
In this note, we give an overview of a new technique for studying Brill--Noether curves in projective space via degeneration. In particular, we give a roadmap to the proof of the Maximal Rank
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References

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In this note, we give an overview of a new technique for studying Brill--Noether curves in projective space via degeneration. In particular, we give a roadmap to the proof of the Maximal Rank
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Building on our earlier results on tropical independence and shapes of divisors in tropical linear series, we give a tropical proof of the maximal rank conjecture for quadrics. We also prove a
The generality of a section of a curve
• Eric Larson
• Mathematics
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This paper considers the following fundamental problem about intersections in projective space: When is the intersection of a (varying) curve with a (fixed) hypersurface a general set of points on
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Let (C, p_1, p_2, \ldots, p_n) be a general marked curve of genus g, and q_1, q_2, ..., q_n \in P^r be a general collection of points. We determine when there exists a nondegenerate degree d map f :
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Let $$C \subset {\mathbb{P}^r}$$ be a general embedding of prescribed degree of a general smooth curve with prescribed genus. Here we prove that either  {h^0}\left(
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• Eric Larson
• Mathematics
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Given $n$ general points $p_1, p_2, \ldots , p_n \in{\mathbb{P}}^r$ it is natural to ask whether there is a curve of given degree $d$ and genus $g$ passing through them; by counting dimensions a