Projective varieties covered by isotrivial families

2011/10/25 by Anupam Bhatnagar, Bhatnagar, Anupam
Mathematics · #13D10 #14D15 #37P55 #Algebraic Geometry (math.AG) #Dynamical Systems (math.DS) #FOS: Mathematics #math.AG #math.DS #msc:13D10 #msc:14D15 #msc:37P55

paper · pdf · doi:10.48550/arxiv.1110.5661

Final Version. To Appear in Proc. of Amer. Math. Soc

arxiv created 2013/01/24 · arxiv updated 2013/01/25

Abstract

Let X,Y be projective schemes over a discrete valuation ring R, where Y is generically smooth and g:X → Y a surjective R-morphism such that g_*O_X = O_Y. We show that if the family X → Spec(R) is isotrivial, then the generic fiber of the family Y → Spec(R) is isotrivial.

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