Comparison of fundamental group schemes of a projective variety and an ample hypersurface

2006/03/13 by Indranil Biswas, Biswas, Indranil, Yogish I. Holla +1 · 1 citation
Mathematics · Physics and Astronomy · #14J60 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.math/0603299

openalex publication_date 2006/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X be a smooth projective variety defined over an algebraically closed field, and let L be an ample line bundle over X. We prove that for any smooth hypersurface D on X in the complete linear system | L^{⊗ d}|, the inclusion map D\hookrightarrow X induces an isomorphism of fundamental group schemes, provided d is sufficiently large and dim X ≥ 3. If dim X = 2, and d is sufficiently large, then the induced homomorphism of fundamental group schemes remains surjective. We give an example to show that the homomorphism of fundamental group schemes induced by the inclusion map of a reduced ample curve in a smooth projective surface is not surjective in general.

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