La monodromie Hamiltonienne des cycles évanescents
| dc.creator | Garay, Mauricio D. | |
| dc.date | 2005-05-11 | |
| dc.date.accessioned | 2026-07-07T05:19:47Z | |
| dc.date.available | 2026-07-07T05:19:47Z | |
| dc.description | We study the monodromy of vanishing cycles for map-germs $f:(C^{2n},0) \to (\CM^k,0)$ whose components are in involution. Although the singular fibres of such maps have non-isolated singularities, it is shown that the regular fibres are $2(n-k)$-connected and that the vanishing homology group of rank $2(n-k)+1$ is freely generated by the vanishing cycles. As corollaries, we get that the multiplicity of the discriminant is equal to the dimension of the vanishing homology group of rank $2(n-k)+1$ and that the Variation operator is an isomorphism. These results are proved under two assumptions: 1. the pyramidality assumptions which states that the singular locus is propagated along the Hamilton flow of the components of $f$ 2. the generic singular fibres should have transverse Morse singularities and their locus should be connected. It is conjectured that outside a set of infinite codimension the first condition holds and that there exists an involutive deformation of $f$ which satisfies condition 2. | |
| dc.description | 13 pages | |
| dc.identifier | https://arxiv.org/abs/math/0505209 | |
| dc.identifier | http://arxiv.org/abs/math/0505209 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75148 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 32S50 | |
| dc.title | La monodromie Hamiltonienne des cycles évanescents | |
| dc.type | text |