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math.AG2024
Two results on the Convex Algebraic Geometry of sets with continuous symmetries
Renato G. Bettiol, Mario Kummer, Ricardo A. E. Mendes
We prove two results on convex subsets of Euclidean spaces invariant under an orthogonal group action. First, we show that invariant spectrahedra admit an equivariant spectrahedral…
math.AG2024
Maximal Mumford Curves from Planar Graphs
Mario Kummer, Bernd Sturmfels, Raluca Vlad
A curve of genus g is maximal Mumford (MM) if it has g+1 ovals and g tropical cycles. We construct full-dimensional families of MM curves in the Hilbert scheme of canonical curves.…
math.CO2024
Three results related to the half-plane property of matroids
Mario Kummer, David Sawall
We settle three problems from the literature on stable and real zero polynomials and their connection to matroid theory. We disprove the weak real zero amalgamation conjecture by S…