Self-dual matroids from canonical curves

TL;DR

This paper explores self-dual matroids derived from canonical curves, analyzing their properties, parametrization, and realization spaces, and provides algorithms for reconstructing curves from configurations.

Contribution

It introduces a comprehensive study of self-dual matroids from canonical curves, including classification, parametrization, and algorithms for curve recovery.

Findings

All self-dual matroids up to rank 5 are tabulated.

The realization spaces of these matroids are investigated.

Algorithms for recovering curves from configurations are explored.

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.