2,264 research outputs found
Higgs bundles and exceptional isogenies
We explore relations between Higgs bundles that result from isogenies between
low-dimensional Lie groups, with special attention to the spectral data for the
Higgs bundles. We focus on isogenies onto and and their
split real forms. Using fiber products of spectral curves, we obtain directly
the desingularizations of the (necessarily singular) spectral curves associated
to orthogonal Higgs bundles. In the case of our construction can be
interpreted as a new description of Recillas' trigonal construction.Comment: Inadvertent omission in Acknowledgements correcte
Rank two quadratic pairs and surface group representations
Let be a compact Riemann surface. A quadratic pair on consists of a
holomorphic vector bundle with a quadratic form which takes values in fixed
line bundle. We show that the moduli spaces of quadratic pairs of rank 2 are
connected under some constraints on their topological invariants. As an
application of our results we determine the connected components of the
-character variety of .Comment: 37 pages, 1 figur
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