Periodicity of Hitchin's Uniformizing Higgs Bundles
R Krishnamoorthy, M Sheng - … Mathematics Research Notices, 2024 - academic.oup.com
R Krishnamoorthy, M Sheng
International Mathematics Research Notices, 2024•academic.oup.com… In [23], we studied the periodicity of the uniformizing Higgs bundle over |${{\mathbb{P}}}^{1}$|
minus four points and its possible relation with the |${{\mathbb{Z}}}$|-lattice structure of the
associated uniformizing representation of |$\pi _{1}$|. In this article, we explore further into
this connection for smooth projective curves. … Property (ii) is predicted by the
aforementioned polystability conjecture, because polystable Higgs bundles over elliptic
curves must be direct sums of line bundles, and we show that, over any smooth projective …
minus four points and its possible relation with the |${{\mathbb{Z}}}$|-lattice structure of the
associated uniformizing representation of |$\pi _{1}$|. In this article, we explore further into
this connection for smooth projective curves. … Property (ii) is predicted by the
aforementioned polystability conjecture, because polystable Higgs bundles over elliptic
curves must be direct sums of line bundles, and we show that, over any smooth projective …
Abstract
Let be a smooth projective curve over . We link the periodicity of Hitchin’s uniformizing Higgs bundle of with the underlying arithmetic geometry of the curve. Some new relations are discovered. We also speculate on the whole class of periodic Higgs bundles.
Oxford University Press