Irregularity of hypergeometric systems via slopes along coordinate subspaces
| dc.creator | Schulze, Mathias | |
| dc.creator | Walther, Uli | |
| dc.date | 2006-08-27 | |
| dc.date | 2008-02-05 | |
| dc.date.accessioned | 2026-07-07T09:55:31Z | |
| dc.date.available | 2026-07-07T09:55:31Z | |
| dc.description | We study the irregularity sheaves attached to the $A$-hypergeometric $D$-module $M_A(β)$ introduced by Gel'fand et al., where $A\in\mathbb{Z}^{d\times n}$ is pointed of full rank and $β\in\mathbb{C}^d$. More precisely, we investigate the slopes of this module along coordinate subspaces. In the process we describe the associated graded ring to a positive semigroup ring for a filtration defined by an arbitrary weight vector $L$ on torus equivariant generators. To this end we introduce the $(A,L)$-umbrella, a simplicial complex determined by $A$ and $L$, and identify its facets with the components of the associated graded ring. We then establish a correspondence between the full $(A,L)$-umbrella and the components of the $L$-characteristic variety of $M_A(β)$. We compute in combinatorial terms the multiplicities of these components in the $L$-characteristic cycle of the associated Euler-Koszul complex, identifying them with certain intersection multiplicities. We deduce from this that slopes of $M_A(β)$ are combinatorial, independent of $β$, and in one-to-one correspondence with jumps of the $(A,L)$-umbrella. This confirms a conjecture of Sturmfels and gives a converse of a theorem of Hotta: $M_A(β)$ is regular if and only if $A$ defines a projective variety. | |
| dc.description | 44 pages, 3 figures, choose PS or PDF to see figures, new Lemma 2.8 fills gap in previous version of Lemma 2.12, error in previous version of Theorem 3.2 repaired by considering L-holonomic modules in Sections 3.2 and 4.2 | |
| dc.identifier | https://arxiv.org/abs/math/0608668 | |
| dc.identifier | http://arxiv.org/abs/math/0608668 | |
| dc.identifier | Duke Math. J. 142,3 (2008), 465-509 | |
| dc.identifier | doi:10.1215/00127094-2008-011 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/166655 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Combinatorics | |
| dc.subject | 13N10; 14M25; 16W70 | |
| dc.title | Irregularity of hypergeometric systems via slopes along coordinate subspaces | |
| dc.type | text |