New criteria for algebraically rectifiable plane curves are introduced by relating them to quadratic differentials, with a generalization to differentials of higher order.
Confocal families of plane algebraic curves
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abstract
We study families of plane algebraic curves sharing the same set of foci. We reformulate confocality via a focal map on equiclassical families and analyze its fibers using deformation theory.
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2026 1verdicts
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Plane rectifiable curves: old and new
New criteria for algebraically rectifiable plane curves are introduced by relating them to quadratic differentials, with a generalization to differentials of higher order.