15 May 2021 A variety that cannot be dominated by one that lifts
Remy van Dobben de Bruyn
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Duke Math. J. 170(7): 1251-1289 (15 May 2021). DOI: 10.1215/00127094-2020-0055


We prove a strong version of a theorem of Siu and Beauville on morphisms to higher genus curves, and we use it to show that if a variety X in characteristic p lifts to characteristic 0, then any morphism XC to a curve of genus g2 can be lifted along. We use this to construct, for every prime p, a smooth projective surface X over F¯p that cannot be rationally dominated by a smooth proper variety Y that lifts to characteristic 0.


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Remy van Dobben de Bruyn. "A variety that cannot be dominated by one that lifts." Duke Math. J. 170 (7) 1251 - 1289, 15 May 2021. https://doi.org/10.1215/00127094-2020-0055


Received: 25 April 2019; Revised: 17 August 2020; Published: 15 May 2021
First available in Project Euclid: 23 March 2021

Digital Object Identifier: 10.1215/00127094-2020-0055

Primary: 14G17
Secondary: 11G25 , 14D06 , 14D15 , 14F35

Keywords: Algebraic Geometry , algebraic surfaces of general type , counterexamples , deformation theory , finite fields , irrational pencils , lifting , positive characteristic

Rights: Copyright © 2021 Duke University Press

Vol.170 • No. 7 • 15 May 2021
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