Betti numbers of the moduli space of rank 3 parabolic Higgs bundles

Details Betti numbers of the moduli space of rank 3 parabolic Higgs bundles Betti numbers of the moduli space of rank 3 parabolic Higgs bundles

2004-11-10

arxiv.org/abs/math/0411242v3

Mathematics

Algebraic Geometry

78 pages. Extended version. Added a section with the fixed determinant case. To appear in Memoirs of the AMS

Scientific paper

We compute the Betti numbers of the moduli space of rank 3 parabolic Higgs
bundles, using Morse theory. A key point is that certain critical submanifolds
of the Morse function can be identified with moduli spaces of parabolic
triples. These moduli spaces come in families depending on a real parameter and
we study their variation with this parameter.

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