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2018-02-24  00:32 hrs.

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

David Mond
University of Warwick


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 a family of involutive ideals 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.




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