Abstract
In the paper, the notion of generalized Fuchsian systems of differential equations with logarithmic singularities along a divisor D on a complex manifold is discussed. It is proved that such a system is characterized by the property of being regular singular along its singular locus in the classical sense. The proof is based on the main properties of logarithmic differential forms and vector fields; it does not use the traditional technique of resolution of singularities by means of which this problem is usually reduced to the study of divisors with normal crossings. In the case where the system in question has singularities along a free Saito divisor, a purely algebraic method of computing the integrability condition in terms of the commutation relations on its coefficient matrices is described.
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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 15, Theory of Functions, 2004.
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Aleksandrov, A.G. Generalized Fuchsian Systems of Differential Equations. J Math Sci 132, 689–699 (2006). https://doi.org/10.1007/s10958-006-0017-x
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DOI: https://doi.org/10.1007/s10958-006-0017-x