Geometry of obstructed equisingular families of projective hypersurfaces

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dc.creatorGourevitch, Anna
dc.creatorGourevitch, Dmitry
dc.date2008-03-13
dc.date2009-03-11
dc.date.accessioned2026-07-07T13:05:20Z
dc.date.available2026-07-07T13:05:20Z
dc.descriptionWe study geometric properties of certain obstructed equisingular families of projective hypersurfaces with emphasis on smoothness, reducibility, being reduced, and having expected dimension. In the case of minimal obstructness, we give a detailed description of such families corresponding to quasihomogeneous singularities. Next we study the behavior of these properties with respect to stable equivalence of singularities. We show that under certain conditions, stabilization of singularities ensures the existence of a reduced component of expected dimension. For minimally obstructed families the whole family becomes irreducible. As an application we show that if the equisingular family of a projective hypersurface H has a reduced component of expected dimension then the deformation of H induced by the linear system |H| is complete with respect to one-parameter deformations.
dc.description30 pages. v2: more detailed explanations. v3: minor corrections, version to appear in the Journal of Pure and Applied Algebra
dc.identifierhttps://arxiv.org/abs/0803.2026
dc.identifierhttp://arxiv.org/abs/0803.2026
dc.identifierJournal of Pure and Applied Algebra 213 (2009), pp. 1865-1889
dc.identifierdoi:10.1016/j.jpaa.2009.02.012
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/227459
dc.subjectAlgebraic Geometry
dc.subject14F17; 14H20; 14B12; 14J70; 14D20
dc.titleGeometry of obstructed equisingular families of projective hypersurfaces
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