Pure Maths Colloquium: Free Divisors coming from Coxeter groups and Singularity Theory
24 October 2011 16:00 in CM221
Free divisors are hypersurfaces whose tangent behaviour is as simple as possible: the ambient vector fields tangent to the divisor form a free module over the ring of functions on the ambient space. Smooth hypersurfaces are obvious examples, but more interesting are singular free
divisors, whose singular set is necessarily of codimension 1. Singularity theory provides a host of intriguing examples, which often appear as discriminants in deformation spaces. The union of the reflecting hyperplanes of a Coxeter group is another example. The talk will explain how to compute the cohomology of the complement from the matrix of coefficients of a basis for the module of tangent vector fields (the so called Logarithmic Comparison Theorem). It will end with a description of a new class of examples associated with representations of algebraic groups and quivers, where the
computation is especially simple.
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