Singular hypersurfaces possessing infinitely many star points
Filip Cools, Marc Coppens
TL;DR
This paper investigates the geometric structure of hypersurfaces with infinitely many star points, proving linearity of certain components and analyzing specific cases for surfaces.
Contribution
It establishes that components of star points' closures are linear and explores the maximal dimension case and surfaces in detail.
Findings
Components of star points' closures are linear.
Characterization of star points on hypersurfaces of degree d>2.
Specific analysis for surfaces (N=3).
Abstract
We prove that a component of the closure of the set of star points on a hypersurface X of degree d>2 in N-dimensional projective space is linear. Afterwards, we focus on the case where the component is of maximal dimension N-2 and the case where X is a surface (i.e. N=3).
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Commutative Algebra and Its Applications · Mathematics and Applications