• 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. 
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  • Mathematics
    Journal of the London Mathematical Society
  • 2016
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Interpolation for Brill–Noether curves in $${\mathbb {P}}^4$$ P 4
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References

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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
Tropical independence II: The maximal rank conjecture for quadrics
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
    Journal of the London Mathematical Society
  • 2016
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
On the Existence of Special Divisors
Let X be a complete nonsingular curve of genus g defined over an algebraically closed field Ic of any characteristic, let J be the jacobian variety. Denote by G;r the set of points of J which are
Interpolation for Restricted Tangent Bundles of General Curves
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 :
On the variety of special linear systems on a general algebraic curve
0. Introduction (a) Statement of the problem and of the main theorem; some references 233 (b) Corollaries of the main theorem 236 (c) Role of the Brill-Noether matrix 238 (d) Heuristic reasoning for
Embeddings of general curves in projective spaces: the range of the quadrics
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(
Interpolation for Curves in Projective Space with Bounded Error
  • Eric Larson
  • Mathematics
    International Mathematics Research Notices
  • 2019
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
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