Hyperbolic Secant Varieties of M-Curves

Publikation: Beitrag in FachzeitschriftForschungsartikelBeigetragenBegutachtung

Beitragende

Abstract

We relate the geometry of curves to the notion of hyperbolicity in real algebraic geometry. A hyperbolic variety is a real algebraic variety that (in particular) admits a real fibered morphism to a projective space whose dimension is equal to the dimension of the variety. We study hyperbolic varieties with a special interest in the case of hypersurfaces that admit a real algebraic ruling. The central part of the paper is concerned with secant varieties of real algebraic curves where the real locus has the maximal number of connected components, which is determined by the genus of the curve. For elliptic normal curves, we further obtain definite symmetric determinantal representations for the hyperbolic secant hypersurfaces, which implies the existence of symmetric Ulrich sheaves of rank one on these hypersurfaces. We also use this to derive better bounds on the size of semidefinite representations for convex hulls of real algebraic curves of genus 1.

Details

OriginalspracheEnglisch
Seiten (von - bis)125-162
Seitenumfang38
Fachzeitschrift Journal für die reine und angewandte Mathematik : the world's oldest mathematical periodical
Jahrgang2022
Ausgabenummer787
PublikationsstatusVeröffentlicht - 2022
Peer-Review-StatusJa

Externe IDs

Scopus 85129275546
WOS 000783649500001
Mendeley 469739a6-bf22-3140-ba9e-eb82e7e9e1cc

Schlagworte

Bibliotheksschlagworte