Monodromy of hypergeometric functions arising from arrangements of hyperplanes
| dc.creator | Kanarek, Herbert | |
| dc.date | 1996-08-26 | |
| dc.date.accessioned | 2026-07-07T09:06:57Z | |
| dc.date.available | 2026-07-07T09:06:57Z | |
| dc.description | Given an arrangement of hyperplanes in $¶^n$, possibly with non-normal crossings, we give a vanishing lemma for the cohomology of the sheaf of $q$-forms with logarithmic poles along our arrangement. We give a basis for the ideal $\cal J$ of relations for the Orlik-Solomon's algebra. Under certain genericity conditions it was shown by H.~Esnault, V.~Schechtman and E.~Viehweg that the cohomology of a local system is given by the Aomoto complex. We generalize this result to a deformation of local systems obtained via a deformation of our arrangement. We calculate the Gauß-Manin connection for this case. We give a basis for the Gauß-Manin bundle for which, with help of the basis for $\cal J$, we give then a method to calculate a representation of this connection. From here, with the results of K-T.~Chen or P.~Deligne, one can calculate the monodromy representation. This gives a generalization of the hypergeometric functions. | |
| dc.description | LaTex file, 33 pages, 6 figures | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9608031 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9608031 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/150198 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Monodromy of hypergeometric functions arising from arrangements of hyperplanes | |
| dc.type | text |