Monodromy invariant Hermitian forms for second order Fuchsian differential equations with four singularities
We study the monodromy invariant Hermitian forms for second order Fuchsian differential equations with four singularities. The moduli space of our monodromy representations can be realized by certain affine cubic surface. In this paper we characterize the irreducible monodromies having the non-degen...
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| Format: | Article |
| Language: | English |
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AGH Univeristy of Science and Technology Press
2022-04-01
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| Series: | Opuscula Mathematica |
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| Online Access: | https://www.opuscula.agh.edu.pl/vol42/3/art/opuscula_math_4216.pdf |
| Summary: | We study the monodromy invariant Hermitian forms for second order Fuchsian differential equations with four singularities. The moduli space of our monodromy representations can be realized by certain affine cubic surface. In this paper we characterize the irreducible monodromies having the non-degenerate invariant Hermitian forms in terms of that cubic surface. The explicit forms of invariant Hermitian forms are also given. Our result may bring a new insight into the study of the Painlevé differential equations. |
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| ISSN: | 1232-9274 |