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arXiv · 2410.08528

Direct image of structure sheaf and parabolic stability

Indranil Biswas·Manish Kumar·A. J. Parameswaran
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Abstract

Let $f : X \rightarrow Y$ be a dominant generically smooth morphism between irreducible smooth projective curves over an algebraically closed field $k$ such that ${\rm Char}(k)> \text{degree}(f)$ if the characteristic of $k$ is nonzero. We prove that $(f_*{\mathcal O}_X)/{\mathcal O}_Y$ equipped with a natural parabolic structure is parabolic polystable. Several conditions are given that ensure that the parabolic vector bundle $(f_*{\mathcal O}_X)/{\mathcal O}_Y$ is actually parabolic stable.

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Indranil Biswas, Manish Kumar, A. J. Parameswaran. 2024-10-11. Direct image of structure sheaf and parabolic stability. https://arxiv.org/abs/2410.08528

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