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Projective varieties covered by isotrivial families


Author: Anupam Bhatnagar
Journal: Proc. Amer. Math. Soc. 142 (2014), 1561-1566
MSC (2010): Primary 14D15; Secondary 13D10, 37P55
DOI: https://doi.org/10.1090/S0002-9939-2014-11966-6
Published electronically: February 13, 2014
MathSciNet review: 3168463
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Abstract: Let $ X,Y$ be projective schemes over a discrete valuation ring $ R$, where $ Y$ is generically smooth and $ g: X \to Y$ is a surjective $ R$-morphism such that $ g_*\mathcal {O}_{X} = \mathcal {O}_{Y}$. We show that if the family $ X \to Spec(R)$ is isotrivial, then the generic fiber of the family $ Y\to Spec(R)$ is isotrivial.


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Additional Information

Anupam Bhatnagar
Affiliation: Department of Mathematics, Borough of Manhattan Community College, 199 Chambers Street, New York, New York 10007
Email: anupambhatnagar@gmail.com

DOI: https://doi.org/10.1090/S0002-9939-2014-11966-6
Keywords: Deformation theory, algebraic dynamics, isotrivial families, descent of varieties
Received by editor(s): December 17, 2011
Received by editor(s) in revised form: June 7, 2012, and June 15, 2012
Published electronically: February 13, 2014
Communicated by: Lev Borisov
Article copyright: © Copyright 2014 American Mathematical Society

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