Claus Scheiderer

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math.AG2025

Smooth hyperbolicity cones are second-order cone representable

Claus Scheiderer

Netzer and Sanyal proved that every smooth hyperbolicity cone is a spectrahedral shadow. We generalize and sharpen this result at the same time, by showing that every Nash-smooth h…

math.AG2024

An elementary proof of Hilbert's theorem on ternary quartics: Some complements

Albrecht Pfister, Claus Scheiderer

In 1888, Hilbert proved that every nonnegative quartic form $f = f (x, y, z)$ with real coefficients is a sum of three squares of quadratic forms. His proof was ahead of its time and us…

math.AG2024

Convex hulls of curves in $n$ -space

Claus Scheiderer

Let $K \subseteq R^{n}$ be a convex semialgebraic set. The semidefinite extension degree $sxdeg (K)$ of $K$ is the smallest number $d$ such that $K$ is a linear ima…

Smooth hyperbolicity cones are second-order cone representable

An elementary proof of Hilbert's theorem on ternary quartics: Some complements

Convex hulls of curves in n-space

Convex hulls of curves in $n$ -space