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Tautological systems and free divisors

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We introduce tautological system defined by prehomogenous actions of reductive algebraic groups. If the complement of the open orbit is a linear free divisor satisfying a certain finiteness condition, we… Click to show full abstract

We introduce tautological system defined by prehomogenous actions of reductive algebraic groups. If the complement of the open orbit is a linear free divisor satisfying a certain finiteness condition, we show that these systems underly mixed Hodge modules. A dimensional reduction is considered and gives rise to one-dimensional differential systems generalizing the quantum differential equation of projective spaces.

Keywords: free divisors; tautological systems; systems free

Journal Title: Advances in Mathematics
Year Published: 2019

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