Nodes on quintic spectrahedra

TL;DR

This paper classifies and explicitly constructs 65 distinct classes of real determinantal surfaces of degree 5 with 20 nodes, advancing understanding of the geometry of quintic spectrahedra.

Contribution

It provides a complete classification of transversal quintic spectrahedra based on node configurations and supplies explicit examples for each class.

Findings

Identified 65 classes of such spectrahedra.

Constructed explicit representatives for each class.

Enhanced understanding of the geometric structure of quintic spectrahedra.

Abstract

We classify transversal quintic spectrahedra by the location of 20 nodes on the respective real determinantal surface of degree 5. We identify 65 classes of such surfaces and find an explicit representative in each of them.