Brill-Noether varieties of k-gonal curves

By Nathan Pflueger. 2016

46 citations recorded by the source corpus.

We consider a general curve of fixed gonality k and genus g. We propose an estimate for the dimension of the variety $W^r_d(C)$ of special linear series on C, by solving an analogous problem in tropical geometry. Using work of Coppens and Martens, we prove that this estimate is exactly correct if k is at least g/5 + 2, and is an upper bound in all other cases. We also completely characterize the cases in which $W^r_d(C)$ has the same dimension as for a general curve of genus g.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/40b93d775bfd8369ec02462f6314d7b664a3f7bc

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In Algebra and Number Theory

1. David Jensen
2. Dhruv Ranganathan

In Computational Theory and Mathematics

1. Dhruv Ranganathan
2. David Jensen

In Geometry and Topology

1. Dhruv Ranganathan
2. David Jensen

Citations in the corpus

• Brill-Noether theory for curves of a fixed gonality (2017, methodology): “Similarly, in [21] and subsequent papers, the tableau corresponding to a divisor of rank A and degree 3 has A + 1 columns and 6 − 3 + A rows, but in [46, 47] this convention is reversed.”