Martin Helsø (UiO): Rational quartic spectrahedra

Abstract: Rational quartic spectrahedra in real 3-space are semialgebraic convex subsets of semidefinite real symmetric (4×4)-matrices, whose boundary admits a rational parameterization. The Zariski closure in complex projective space of the boundary is a symmetroid. If the symmetroid has only simple double points as singularities, it is irrational, in fact birational to a K3-surface, so rational symmetroids are special. Rational quartic symmetroids have a a triple point, an elliptic double point or is singular along a curve. Reporting on common work in progress with Kristian Ranestad, I shall give several examples and first results towards a classification.