Genuinely ramified maps and pseudo-stable vector bundles
Indranil Biswas, A. J. Parameswaran

TL;DR
This paper investigates the properties of pseudo-stable vector bundles under genuinely ramified maps between algebraic varieties, establishing surjectivity of certain fundamental group homomorphisms and stability preservation.
Contribution
It proves the surjectivity of the induced homomorphism between affine group schemes and shows that pseudo-stability is preserved under pullback and subbundle conditions.
Findings
Surjectivity of the homomorphism between affine group schemes induced by the map.
Pseudo-stability of the pullback of a pseudo-stable vector bundle.
Existence of a pseudo-stable subbundle W such that f^*W = F.
Abstract
Let and be irreducible normal projective varieties, of same dimension, defined over an algebraically closed field, and let be a finite generically smooth morphism such that the corresponding homomorphism between the \'etale fundamental groups is surjective. Fix a polarization on and equip with the pulled back polarization. For a point , let (respectively, ) be the affine group scheme given by the neutral Tannakian category defined by the strongly pseudo-stable vector bundles of degree zero on (respectively, ). We prove that the homomorphism induced by is surjective. Let be a pseudo-stable vector bundle on and a pseudo-stable subbundle with . We…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Alkaloids: synthesis and pharmacology
