Direct Image of Structure Sheaf and Parabolic Stability
Vol. 32 (2025), No. 2, Page 241–256.
Biswas, Indranil; Kumar, Manish; Parameswaran, A. J.
Direct Image of Structure Sheaf and Parabolic Stability
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Abstract:
Let $f\, :\, X\, \longrightarrow\, Y$ 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.
Keywords: Parabolic stability, direct image, socle, Harder-Narasimhan filtration.
Mathematics Subject Classification (2020): 14H30, 14H60, 14E20.
Mathematical Reviews Number: MR4973975
Received: 2024-06-14
