Ramified covering maps of singular curves and stability of pulled back bundles

Authors

Indranil Biswas, Shiv Nadar Institution of Eminence deemed to be University
Manish Kumar, Indian Statistical Institute Bangalore
A. J. Parameswaran, Tata Institute of Fundamental Research, Mumbai

Article Type

Research Article

Publication Title

Rendiconti Del Circolo Matematico Di Palermo

Abstract

Let f:X⟶Y be a generically smooth nonconstant morphism between irreducible projective curves, defined over an algebraically closed field, which is étale on an open subset of Y that contains both the singular locus of Y and the image, in Y, of the singular locus of X. We prove that the following statements are equivalent: The homomorphism of étale fundamental groups (Formula presented.) induced by f is surjective. There is no nontrivial étale covering ϕ:Y^′⟶Y admitting a morphism q:X⟶Y^′ such that ϕ∘q=f. The fiber product X×YX is connected. dimH⁰(X,f^∗f∗OX)=1. OY⊂f∗OX is the maximal semistable subsheaf. The pullback f^∗E of every stable sheaf E on Y is also stable.

First Page

1555

Last Page

1565

DOI

10.1007/s12215-024-00999-4

Publication Date

6-1-2024

Recommended Citation

Biswas, Indranil; Kumar, Manish; and Parameswaran, A. J., "Ramified covering maps of singular curves and stability of pulled back bundles" (2024). Journal Articles. 5027.
https://digitalcommons.isical.ac.in/journal-articles/5027