On the Stability of Pulled Back Parabolic Vector Bundles
Vol. 29 (2022), No. 3, Page 359-382.
Biswas, Indranil; Kumar, Manish; Parameswaran, A. J.
On the Stability of Pulled Back Parabolic Vector Bundles
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Abstract:
Take an irreducible smooth projective curve $X$ defined over an algebraically closed field of characteristic zero, and fix finitely many distinct point $D\, =\, \{x_1,\, \cdots,\, x_n\}$ of it; for each point $x\, \in\, D$ fix a positive integer $N_x$. Take a nonconstant map $f\, :\, Y\, \longrightarrow \, X$ from an irreducible smooth projective curve. We construct a natural subbundle $\mathcal{F}\, \subset\, f_*{\mathcal O}_Y$ using $(D,\, \{N_x\}_{x\in D})$. Let $E_*$ be a stable parabolic vector bundle whose parabolic weights at each $x\, \in\, D$ are integral multiples of $\frac{1}{N_x}$. We prove that the pullback $f^*E_*$ is also parabolic stable, if ${\rm rank}(\mathcal{F})\,=\, 1$.
Keywords: arabolic bundle, stability, orbifold, canonical subsheaf.
Mathematics Subject Classification (2010): 14H30, 14H60, 14E20.
Mathematical Reviews Number: MR4515054
Received: 2022-06-20
