Logahoric Higgs Torsors for a Complex Reductive Group

2021/07/05 by Kydonakis, Georgios, Sun, Hao, Zhao, Lutian · 1 citation
#14D23 #14L15 #32Q26 (Primary) #53D17 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2107.01977

Abstract

In this article, a logahoric Higgs torsor is defined as a parahoric torsor with a logarithmic Higgs field. For a connected complex reductive group G, we introduce a notion of stability for logahoric G_{\boldsymbolθ}-Higgs torsors on a smooth algebraic curve X, where G_{\boldsymbolθ} is a parahoric group scheme on X. In the case when the group G is the general linear group \rm GL_n, we show that the stability condition of a parahoric torsor is equivalent to the stability of a parabolic bundle. A correspondence between semistable logahoric G_{\boldsymbolθ}-Higgs torsors and semistable equivariant logarithmic G-Higgs bundles allows us to construct the moduli space explicitly. This moduli space is shown to be equipped with an algebraic Poisson structure.

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• Level structures on parahoric torsors and complete integrability

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