Nonzero Constant Wronskians of Polynomials and Laurent Polynomials, and Geometric Consequences
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913562574716928 |
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| author | Hermoso, Carlos Alcázar, Juan Gerardo |
| author_facet | Hermoso, Carlos Alcázar, Juan Gerardo |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_18867 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nonzero Constant Wronskians of Polynomials and Laurent Polynomials, and Geometric Consequences Hermoso, Carlos Alcázar, Juan Gerardo Algebraic Geometry 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. |
| title | Nonzero Constant Wronskians of Polynomials and Laurent Polynomials, and Geometric Consequences |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2410.18867 |