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On the local monodromy of $A$-hypergeometric functions and some monodromy invariant subspaces
- Source :
- Revista Matemática Iberoamericana. 35:949-961
- Publication Year :
- 2019
- Publisher :
- European Mathematical Society - EMS - Publishing House GmbH, 2019.
-
Abstract
- We obtain an explicit formula for the characteristic polynomial of the local monodromy of $A$-hypergeometric functions with respect to small loops around a coordinate hyperplane $x_i =0$. This formula is similar to the one obtained by Ando, Esterov and Takeuchi for the local monodromy at infinity. Our proof is combinatorial and can be adapted to provide an alternative proof for the latter formula as well. On the other hand, we also prove that the solution space at a nonsingular point of certain irregular and irreducible $A$--hypergeometric $D$--modules has a nontrivial global monodromy invariant subspace.<br />Comment: 13 pages, 1 figure. Section 5 changed since previous version contained a gap. Final version, accepted for publication in Revista Matem\'atica Iberoamericana
- Subjects :
- Pure mathematics
General Mathematics
Invariant subspace
32C38, 33C70, 32S40
Linear subspace
law.invention
Mathematics - Algebraic Geometry
Mathematics::Algebraic Geometry
Invertible matrix
Monodromy
Hyperplane
law
FOS: Mathematics
Invariant (mathematics)
Hypergeometric function
Algebraic Geometry (math.AG)
Mathematics
Characteristic polynomial
Subjects
Details
- ISSN :
- 02132230
- Volume :
- 35
- Database :
- OpenAIRE
- Journal :
- Revista Matemática Iberoamericana
- Accession number :
- edsair.doi.dedup.....13164cdc806651be85b706638911999b