{"ID":2868183,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.17121","arxiv_id":"2509.17121","title":"Smooth hyperbolicity cones are second-order cone representable","abstract":"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 hyperbolicity cone is even second-order cone representable (socr). The result is proved as a consequence of our second theorem, according to which every compact convex semialgebraic set with Nash-smooth boundary of strict positive curvature is socr. The proof uses the technique of tensor evaluation.","short_abstract":"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 hyperbolicity cone is even second-order cone representable (socr). The result is proved as a consequence of our second theorem, according to...","url_abs":"https://arxiv.org/abs/2509.17121","url_pdf":"https://arxiv.org/pdf/2509.17121v2","authors":"[\"Claus Scheiderer\"]","published":"2025-09-21T15:22:06Z","proceeding":"math.AG","tasks":"[\"math.AG\",\"math.OC\"]","methods":"[]","has_code":false}