@article{Helsø_Ranestad_2021, title={Rational quartic spectrahedra}, volume={127}, url={https://www.mscand.dk/article/view/121456}, DOI={10.7146/math.scand.a-121456}, abstractNote={<p>Rational quartic spectrahedra in $3$-space are semialgebraic convex subsets in $\mathbb{R} ^3$ of semidefinite, real symmetric $(4 \times 4)$-matrices, whose boundary admits a rational parameterization. The Zariski closure in $\mathbb{C}\mathbb{P} ^3$ of the boundary of a rational spectrahedron is a rational complex symmetroid. We give necessary conditions on the configurations of singularities of the corresponding real symmetroids in $\mathbb{R} \mathbb{P} ^3$ of rational quartic spectrahedra. We provide an almost exhaustive list of examples realizing the configurations, and conjecture that the missing example does not occur.</p>}, number={1}, journal={MATHEMATICA SCANDINAVICA}, author={Helsø, Martin and Ranestad, Kristian}, year={2021}, month={Feb.}, pages={79–99} }