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arXiv · 1703.03057

Gauss-Manin systems of families of Laurent polynomials and A-hypergeometric systems

Thomas Reichelt·Uli Walther
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Abstract

In this note we study families of Gauss-Manin systems arising from Laurent polynomials with parametric coefficients under projection to the parameter space. For suitable matrices of exponent vectors, we exhibit a natural four-term exact sequence for which we then give an interpretation via generalized A-hypergeometric systems. We determine the extension groups from the parameter sheaf to the middle term of this sequence and show that the four-term sequence does not split. Auxiliary results include the computation of Ext and Tor groups of A-hypergeometric systems against the parameter sheaf.

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Thomas Reichelt, Uli Walther. 2017-03-08. Gauss-Manin systems of families of Laurent polynomials and A-hypergeometric systems. https://arxiv.org/abs/1703.03057

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