Homology groups of spaces of non-resultant quadratic polynomial systems in R^3
Victor A. Vassiliev
TL;DR
This paper computes the rational homology groups of spaces consisting of non-resultant homogeneous quadratic polynomial systems in three-dimensional real space, providing insights into their topological structure.
Contribution
It introduces a method to calculate the rational homology groups of these polynomial system spaces, a novel contribution to algebraic topology and polynomial system analysis.
Findings
Determined the rational homology groups explicitly.
Revealed topological properties of non-resultant quadratic systems.
Provided a framework for analyzing similar polynomial spaces.
Abstract
We calculate rational homology groups of spaces of non-resultant (i.e. having no non-trivial common zeros) systems of homogemeous quadratic polynomials in R^3
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Algebraic Geometry and Number Theory · Polynomial and algebraic computation