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arXiv · 1903.11347

System of Hodge Bundles and Generalized Opers on Smooth Projective Varieties

Suratno Basu·Arjun Paul·Arideep Saha
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Abstract

Let $k$ be an algebraically closed field of any characteristic. Let $X$ be a polarized irreducible smooth projective algebraic variety over $k$. We give criterion for semistability and stability of system of Hodge bundles on $X$. We define notion of generalized opers on $X$, and prove semistability of the Higgs bundle associated to generalized opers. We also show that existence of partial oper structure on a vector bundle $E$ together with a connection $\nabla$ over $X$ implies semistability of the pair $(E, \nabla)$.

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Suratno Basu, Arjun Paul, Arideep Saha. 2019-03-27. System of Hodge Bundles and Generalized Opers on Smooth Projective Varieties. https://doi.org/10.1016/j.geomphys.2019.103484

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