Abstract
Let M be an irreducible smooth projective variety defined over . Let ϖ(M, x 0) be the fundamental group scheme of M with respect to a base point x 0. Let G be a connected semisimple linear algebraic group over . Fix a parabolic subgroup P ⊊ G, and also fix a strictly antidominant character χ of P. Let E G → M be a principal G-bundle such that the associated line bundle E G (χ) → E G /P is numerically effective. We prove that E G is given by a homomorphism ϖ(M, x 0) → G. As a consequence, there is no principal G-bundle E G → M such that degree(ϕ*E G (χ)) > 0 for every pair (Y, ϕ), where Y is an irreducible smooth projective curve, and ϕ: Y → E G /P is a nonconstant morphism.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
