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Stratifications on the Moduli Space of Higgs Bundles
The moduli space of Higgs bundles has two stratifications. The Bia lynickiBirula stratification comes from the action of the non-zero complex numbers by multiplication on the Higgs field, and the Shatz stratification arises ...
Geometric goodness of fit measure to detect patterns in data point clouds
The curse of dimensionality is a commonly encountered problem in statistics and data analysis. Variable sensitivity analysis methods are a well studied and established set of tools designed to overcome these sorts of ...
Geometrical correlation indices using homological constructions on manifolds
Abstract The course of dimensionality is a common problem in statistics and data analysis. Variable sensitivity analysis methods are a well studied and established set of tools designed to overcome these sorts of problems. ...
Variations of Hodge Structures of Rank Three k-Higgs Bundles and Moduli Spaces of Holomorphic Triples
There is an isomorphism between the moduli spaces of σ-stable holomorphic triples and some of the critical submanifolds of the moduli space of k-Higgs bundles of rank three, whose elements (E, ϕk ) correspond to variations ...
Stratifications on the Nilpotent Cone of the moduli space of Hitchin pairs
We consider the problem of finding the limit at infinity (corresponding to the downward Morse flow) of a Higgs bundle in the nilpotent cone under the natural C ∗ -action on the moduli space. For general rank we provide ...
A brief survey of Higgs bundles
Un estudio conciso de fibrados de Higgs
Considering a compact Riemann surface of genus greater or equal than two, a Higgs bundle is a pair composed of a holomorphic bundle over the Riemann surface, joint with an auxiliar vector field, so-called Higgs field. This ...