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arXiv · 2212.05910

Self-dual matroids from canonical curves

Alheydis Geiger·Sachi Hashimoto·Bernd Sturmfels·Raluca Vlad
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Abstract

Self-dual configurations of 2n points in a projective space of dimension n-1 were studied by Coble, Dolgachev-Ortland, and Eisenbud-Popescu. We examine the self-dual matroids and self-dual valuated matroids defined by such configurations, with a focus on those arising from hyperplane sections of canonical curves. These objects are parametrized by the self-dual Grassmannian and its tropicalization. We tabulate all self-dual matroids up to rank 5 and investigate their realization spaces. Following Bath, Mukai, and Petrakiev, we explore algorithms for recovering a curve from the configuration. A detailed analysis is given for self-dual matroids arising from graph curves.

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Alheydis Geiger, Sachi Hashimoto, Bernd Sturmfels, Raluca Vlad. 2022-12-12. Self-dual matroids from canonical curves. https://arxiv.org/abs/2212.05910

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