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arXiv · 2410.18867

Nonzero Constant Wronskians of Polynomials and Laurent Polynomials, and Geometric Consequences

Carlos Hermoso·Juan Gerardo Alcázar
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Abstract

We characterize the polynomials $p_1(t), ... , p_n(t)$ whose Wronskian $W(p_1, ... , p_n)$ is a nonzero constant. Then, we generalize our results to characterize the Laurent polynomials with the same property. Finally, for rational functions we prove an impossibility result for $n=2$, and pose the case $n \geq 3$ as an open question, although we suggest an impossibility conjecture. Some geometric consequences are derived, especially in the case of polynomials.

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Carlos Hermoso, Juan Gerardo Alcázar. 2024-10-24. Nonzero Constant Wronskians of Polynomials and Laurent Polynomials, and Geometric Consequences. https://arxiv.org/abs/2410.18867

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