Stability of pencils of plane sextics and Halphen pencils of index two
Aline Zanardini
TL;DR
This paper investigates the stability of pencils of plane sextic curves using geometric invariant theory, providing a comprehensive description of the stability conditions for Halphen pencils of index two.
Contribution
It offers a complete geometric characterization of the stability of Halphen pencils of index two, advancing understanding in the classification of such algebraic structures.
Findings
Complete description of stability conditions for Halphen pencils of index two
Geometric criteria for stability of pencils of plane sextics
Enhanced classification framework for algebraic pencils
Abstract
We study the stability of pencils of plane sextics in the sense of geometric invariant theory. In particular, we obtain a complete and geometric description of the stability of Halphen pencils of index two.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Differential Equations and Dynamical Systems · Advanced Topics in Algebra