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The intersection form, logarithmic vector fields, and the Severi strata in the discriminant of a plane curve singularity

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Authors : Mond, David (Author of the conference)
CIRM (Publisher )

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Abstract : This talk will describe ongoing joint work with Paul Cadman and Duco van Straten, based on the PhD thesis of the former. Givental and Varchenko used the period mapping to pull back the intersection form on the Milnor fibre of an irreducible plane curve singularity $C$, and thereby define a symplectic structure on the base space of a miniversal deformation. We show how to combine this with a symmetric basis for the module of vector fields tangent to the discriminant, to produce involutive ideals $I_k$ which define the strata of parameter values $u$ such that $\delta(C_u)\leq k$. In the process we find an unexpected Lie algebra and a still mysterious canonical deformation of the module structure of the critical space over the discriminant. Much of this work is experimental - a crucial gap in understanding still needs bridging.

MSC Codes :
14H20 - Singularities, local rings [See also 13Hxx, 14B05]
14H50 - Plane and space curves
32S30 - Deformations of singularities; vanishing cycles

    Information on the Video

    Film maker : Hennenfent, Guillaume
    Language : English
    Available date : 16/03/15
    Conference Date : 03/03/15
    Subseries : Research talks
    arXiv category : Algebraic Geometry
    Mathematical Area(s) : Algebraic & Complex Geometry
    Format : MP4 (.mp4) - HD
    Video Time : 00:49:36
    Targeted Audience : Researchers
    Download : https://videos.cirm-math.fr/2015-03-03_Mond.mp4

Information on the Event

Event Title : Geometry of singular spaces and maps / Géométrie des espaces et applications singuliers
Event Organizers : Brasselet, Jean-Paul ; Pichon, Anne
Dates : 02/03/15 - 06/03/15
Event Year : 2015
Event URL : https://conferences.cirm-math.fr/1478.html

Citation Data

DOI : 10.24350/CIRM.V.18719103
Cite this video as: Mond, David (2015). The intersection form, logarithmic vector fields, and the Severi strata in the discriminant of a plane curve singularity. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18719103
URI : http://dx.doi.org/10.24350/CIRM.V.18719103

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