Projective varieties covered by isotrivial families
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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.References
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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
- 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
- © Copyright 2014 American Mathematical Society
- 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
- MathSciNet review: 3168463