Computing Moment Maps of Hypersurfaces using MAXIMA
Dun Liang
TL;DR
This paper demonstrates how Maxima software can be used to compute moment matrices of hypersurfaces and analyze the stability of plane cubics and quartics using the Hilbert-Mumford criterion.
Contribution
It introduces a method for computing moment matrices and stability criteria of algebraic curves using Maxima, providing practical tools for algebraic geometry research.
Findings
Computed moment matrices for hypersurfaces.
Determined stability of plane cubics and quartics.
Provided explicit stability results for these curves.
Abstract
We use Maxima to compute the moment matrices of hypersurfaces. After that, we compute the Hilbert-Mumford numerical criterion for plane cubics and plane quartics, and give the stability of these curves.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Polynomial and algebraic computation · Advanced Topics in Algebra