On the Stability of Pulled Back Parabolic Vector Bundles

Authors

Indranil Biswas, Tata Institute of Fundamental Research, Mumbai
Manish Kumar, Indian Statistical Institute Bangalore
A. J. Parameswaran, Tata Institute of Fundamental Research, Mumbai

Article Type

Research Article

Publication Title

Journal of Mathematical Sciences (Japan)

Abstract

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.

First Page

359

Last Page

382

Publication Date

1-1-2022

Recommended Citation

Biswas, Indranil; Kumar, Manish; and Parameswaran, A. J., "On the Stability of Pulled Back Parabolic Vector Bundles" (2022). Journal Articles. 3295.
https://digitalcommons.isical.ac.in/journal-articles/3295