A Perturbation Approach to Inverting Projective Degenerate Quadrics and Recovering Lost Geometric Information
Year: 2026
Type: article
Abstract: This article presents a general perturbation approach to retrieving geometric information about the duals of degenerate quadrics obscured by the singular matrices that represent them. By embedding singular quadrics within a one-parameter family of neighbouring non-degenerate quadrics, and then applying standard techniques from analytic perturbation theory, we rigorously isolate the finite remainder from the singular pole residue to extract well-defined pseudo-distance metrics and polarity maps, and reveal how the degenerate limit of this family of non-degenerate quadrics retains an ``asymptotic memory'' of the directions of the perturbation matrices.
Author: Foo, RongHan Dominic
Institution: Western Illinois University
Language: English
Topic: Mathematics and Applications
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212384117
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