Fine polar invariants of minimal singularities of surface

dc.creatorBondil, Romain
dc.date2004-01-30
dc.date.accessioned2026-07-07T05:04:59Z
dc.date.available2026-07-07T05:04:59Z
dc.descriptionWe consider the polar curves $\PSO$ arising from generic projections of a germ $(S,0)$ of complex surface singularity onto $\C^2$. Taking $(S,0)$ to be a minimal singularity of normal surface (i.e. a rational singularity with reduced tangent cone), we give the $δ$-invariant of these polar curves, as well as the equisingularity-type of their generic plane projections, which are also the discriminants of generic projections of $(S,0)$. These two (equisingularity)-data for $\PSO$ are described in term, on the one side of the geometry of the tangent cone of $(S,0)$ and on the other side of the limit-trees introduced by T. de Jong and D. van Straten for the deformation theory of these minimal singularities. These trees give a combinatorial device for the description of the polar curve which makes it much clearer than in our previous Note on the subject. This previous work mainly relied on a result of M. Spivakovsky. Here we give a geometrical proof via deformations (on the tangent cone, and what we call Scott deformations) and blow-ups, although we need Spivakovsky's result at some point, extracting some other consequences of it along the way.
dc.descriptionJanvier 2004
dc.identifierhttps://arxiv.org/abs/math/0401434
dc.identifierhttp://arxiv.org/abs/math/0401434
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/70017
dc.subjectAlgebraic Geometry
dc.subjectPrimary - 32S15, 32S25; Secondary - 14H20, 14B07
dc.titleFine polar invariants of minimal singularities of surface
dc.typetext

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