Duke Mathematical Journal

Chern slopes of surfaces of general type in positive characteristic

Giancarlo Urzúa

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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.

Article information

Duke Math. J., Volume 166, Number 5 (2017), 975-1004.

Received: 23 September 2015
Revised: 2 July 2016
First available in Project Euclid: 15 December 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14J10: Families, moduli, classification: algebraic theory
Secondary: 14C22: Picard groups 14F35: Homotopy theory; fundamental groups [See also 14H30] 14J29: Surfaces of general type

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


Urzúa, Giancarlo. Chern slopes of surfaces of general type in positive characteristic. Duke Math. J. 166 (2017), no. 5, 975--1004. doi:10.1215/00127094-3792596. https://projecteuclid.org/euclid.dmj/1481771254

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