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Cameral covers and Higgs bundles: additive, multiplicative, and elliptic.
Algebraic Geometry and Number Theory| Speaker: | Dima Arinkin, University of Wisconsin, Madison |
| Location: | 2112 MSB |
| Start time: | Wed, Apr 3 2019, 1:10PM |
Description
Higgs bundles are natural geometric objects that have been studied from many different directions. One of the key tools is the Hitchin fibration, which is the geometric version of a fundamental idea from linear algebra: the data (Higgs bundle) is split into spectral data ('eigenvalues') and spacial data (`eigenspaces'). A further development of this idea is the theory of cameral covers due to R.Donagi and D.Gaitsgory.
In my talk, I will extend the theory of cameral covers in two directions: to Higgs fields that need not be regular, and to different kinds of Higgs bundles, such as 'group-valued' Higgs bundles. This allows us to treat, in a uniform way, various `Higgs bundle-like' objects, such as usual or group-valued Higgs bundles, semistable bundles on an elliptic curve, and perhaps even the space of regular connections on a punctured disk.