Article
Irregular hypergeometric D-modules
Author/s | Fernández Fernández, María Cruz |
Department | Universidad de Sevilla. Departamento de álgebra |
Publication Date | 2010-08-01 |
Deposit Date | 2016-06-08 |
Published in |
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Abstract | We study the irregularity of hypergeometric D-modules MA(β) via the
explicit construction of Gevrey series solutions along coordinate subspaces
in X = C n. As a consequence, we prove that along coordinate hyperplanes
the ... We study the irregularity of hypergeometric D-modules MA(β) via the explicit construction of Gevrey series solutions along coordinate subspaces in X = C n. As a consequence, we prove that along coordinate hyperplanes the combinatorial characterization of the slopes of MA(β) given by M. Schulze and U. Walther in [25] still holds for any full rank integer matrix A. We also provide a lower bound for the dimensions of the spaces of Gevrey solutions along coordinate subspaces in terms of volumes of polytopes and prove the equality for very generic parameters. Holomorphic solutions outside the singular locus of MA(β) can be understood as Gevrey solutions of order one along X at generic points and so they are included as a particular case. |
Funding agencies | Ministerio de Educación y Ciencia (MEC). España Junta de Andalucía |
Project ID. | AP2005-2360
MTM2007-64509 FQM333 |
Citation | Fernández Fernández, M.C. (2010). Irregular hypergeometric D-modules. Advances in Mathematics, 224 (5), 1735-1764. |
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