On the Stability of Pulled Back Parabolic Vector Bundles

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Research Article

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Journal of Mathematical Sciences (Japan)


Take an irreducible smooth projective curve X defined over an algebraically closed field of characteristic zero, and fix finitely many distinct point D = {x1, ···, xn} of it; for each point x ∈ D fix a positive integer Nx. Take a nonconstant map f : Y −→ X from an irreducible smooth projective curve. We construct a natural subbundle F ⊂ f∗OY using (D, {Nx}x∈D). Let E∗ be a stable parabolic vector bundle whose parabolic weights at each x ∈ D are integral multiples of N1x. We prove that the pullback f∗E∗ is also parabolic stable, if rank(F) = 1.

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