Self-Dual Matroids from Canonical Curves

IF 0.7 4区数学 Q2 MATHEMATICS

Experimental Mathematics Pub Date : 2022-12-12 DOI:10.1080/10586458.2023.2239282

Alheydis Geiger, Sachi Hashimoto, B. Sturmfels, R. Vlad

引用次数: 2

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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正则曲线中的自对偶拟阵

Coble、Dolgachev-Ortland和Eisenbud-Popescu研究了n-1维投影空间中2n个点的自对偶构型。我们研究了由这种构型定义的自对偶拟阵和自对偶赋值拟阵，重点讨论了正则曲线的超平面截面产生的自对偶拟阵。这些目标是由自对偶格拉斯曼及其热带化参数化。我们将所有5级以下的自对偶拟阵制表，并研究它们的实现空间。继Bath, Mukai和Petrakiev之后，我们探索了从配置中恢复曲线的算法。详细分析了由图曲线产生的自对偶拟阵。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Experimental Mathematics 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Experimental Mathematics publishes original papers featuring formal results inspired by experimentation, conjectures suggested by experiments, and data supporting significant hypotheses. Experiment has always been, and increasingly is, an important method of mathematical discovery. (Gauss declared that his way of arriving at mathematical truths was "through systematic experimentation.") Yet this tends to be concealed by the tradition of presenting only elegant, fully developed, and rigorous results. Experimental Mathematics was founded in the belief that theory and experiment feed on each other, and that the mathematical community stands to benefit from a more complete exposure to the experimental process. The early sharing of insights increases the possibility that they will lead to theorems: An interesting conjecture is often formulated by a researcher who lacks the techniques to formalize a proof, while those who have the techniques at their fingertips have been looking elsewhere. Even when the person who had the initial insight goes on to find a proof, a discussion of the heuristic process can be of help, or at least of interest, to other researchers. There is value not only in the discovery itself, but also in the road that leads to it.