1 April 2017 Chern slopes of surfaces of general type in positive characteristic
Giancarlo Urzúa
Duke Math. J. 166(5): 975-1004 (1 April 2017). DOI: 10.1215/00127094-3792596


Let k be an algebraically closed field of characteristic p>0, and let C be a nonsingular projective curve over k. We prove that for any real number x2, there are minimal surfaces of general type X over k such that (a) c12(X)>0, c2(X)>0, (b) π1e´t(X)π1e´t(C), and (c) c12(X)/c2(X) is arbitrarily close to x. In particular, we show the density of Chern slopes in the pathological Bogomolov–Miyaoka–Yau interval (3,) for any given p. Moreover, we prove that for C=P1 there exist surfaces X as above with H1(X,OX)=0, that is, with Picard scheme equal to a reduced point. In this way, we show that even surfaces with reduced Picard scheme are densely persistent in [2,) for any given p.


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Giancarlo Urzúa. "Chern slopes of surfaces of general type in positive characteristic." Duke Math. J. 166 (5) 975 - 1004, 1 April 2017. https://doi.org/10.1215/00127094-3792596


Received: 23 September 2015; Revised: 2 July 2016; Published: 1 April 2017
First available in Project Euclid: 15 December 2016

zbMATH: 06707167
MathSciNet: MR3626568
Digital Object Identifier: 10.1215/00127094-3792596

Primary: 14J10
Secondary: 14C22 , 14F35 , 14J29

Keywords: Bogomolov–Miyaoka–Yau inequality , Chern numbers , étale fundamental group , Picard scheme , positive characteristic , surfaces of general type

Rights: Copyright © 2017 Duke University Press


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Vol.166 • No. 5 • 1 April 2017
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