La monodromie Hamiltonienne des cycles évanescents

dc.creatorGaray, Mauricio D.
dc.date2005-05-11
dc.date.accessioned2026-07-07T05:19:47Z
dc.date.available2026-07-07T05:19:47Z
dc.descriptionWe 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.description13 pages
dc.identifierhttps://arxiv.org/abs/math/0505209
dc.identifierhttp://arxiv.org/abs/math/0505209
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/75148
dc.subjectAlgebraic Geometry
dc.subject32S50
dc.titleLa monodromie Hamiltonienne des cycles évanescents
dc.typetext

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