Genuinely ramified maps and pseudo-stable vector bundles

Abstract

Let X and Y be irreducible normal projective varieties, of same dimension, defined over an algebraically closed field, and let f:Y⟶X be a finite generically smooth morphism such that the corresponding homomorphism between the étale fundamental groups f∗:π1et(Y)⟶π1et(X) is surjective. Fix a polarization on X and equip Y with the pulled-back polarization. For a point y0∈Y, let ϖ(Y,y0) (resp. ϖ(X,f(y0))) be the affine group scheme given by the neutral Tannakian category defined by the strongly pseudo-stable vector bundles of degree zero on Y (resp. X). We prove that the homomorphism ϖ(Y,y0)⟶ϖ(X,f(y0)) induced by f is surjective. Let E be a pseudo-stable vector bundle on X and F⊂f∗E a pseudo-stable subbundle with μ(F)=μ(f∗E). We prove that f∗E is pseudo-stable and there is a pseudo-stable subbundle W⊂E such that f∗W=F as subbundles of f∗E.

Locations

• Illinois Journal of Mathematics - View
• arXiv (Cornell University) - View - PDF