Arrangements with Isolated Non Noraml Crossings.
Topology of Arrangements and Applications
October 06,2004 11:00 AM to 11:50 AM
Speakers:
Libgober, Anatoly
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Summary: |
The lecture concentrates on finding a high dimensional generalization of line arrangements which have interesting characteristic varieties. The focus is on arrangements of hyperplanes having only isolated non-normal crossings. For such arrangements the fundamental group is abelian and the homotopy groups are trivial in dimensions which are smaller than the dimension of hyperplanes. The most interesting homotopy groups appear in the dimension equal to the dimesion of hyperplanes. This homotopy group is affected by the multiplicities of non normal crossings in arrangements, as well as by the global information about non-normal crossings. A high dimensional
generalization of the Ceva arrangement is presented for which the arrangement is formed by reducible memebers of a net of quadrics
in projective 3-space and for which the second homotopy group of the complement is non trival. Further, it even has a 3-dimensional support
considered as a module over the group ring of the fundamental group. |
Keywords: |
Hyperplane Arrangements;Alexander Invariants. |
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Lecture #10703
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