Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

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


Authors: Indranil Biswas and Yogish I. Holla
Journal: J. Algebraic Geom. 16 (2007), 547-597
DOI: https://doi.org/10.1090/S1056-3911-07-00449-3
Published electronically: March 20, 2007
MathSciNet review: 2306280
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Abstract | References | Additional Information

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 $ \vert L^{\otimes d}\vert$, the inclusion map $ D\hookrightarrow X$ induces an isomorphism of fundamental group schemes, provided $ d$ is sufficiently large and $ \dim X \, \geq\, 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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Additional Information

Indranil Biswas
Affiliation: School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India
Email: indranil@math.tifr.res.in

Yogish I. Holla
Affiliation: School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India
Email: yogi@math.tifr.res.in

DOI: https://doi.org/10.1090/S1056-3911-07-00449-3
Received by editor(s): February 16, 2006
Received by editor(s) in revised form: February 20, 2006
Published electronically: March 20, 2007

American Mathematical Society