Positive Geometries from Cubic Surfaces

TL;DR

This paper explores positive geometries derived from cubic surfaces, analyzing their structure, combinatorial properties, and canonical forms across various dimensions.

Contribution

It introduces a new perspective on cubic surfaces through positive geometry, examining their arrangements, ranks, and forms in multiple dimensions.

Findings

Identifies positive geometries associated with cubic surfaces in dimensions two, three, and four.

Analyzes the combinatorial rank of positive arrangements on these surfaces.

Studies the canonical forms related to these positive geometries.

Abstract

We present a study of cubic surfaces from the novel perspective of positive geometry. Our positive geometries have dimension two (the surface minus its 27 lines), dimension three (its complement in 3-space), and dimension four (the moduli space). In each case we explore the positive arrangement, its combinatorial rank, and the canonical forms.