Let be an algebraically closed field of characteristic , and let be a nonsingular projective curve over . We prove that for any real number , there are minimal surfaces of general type over such that (a) , , (b) , and (c) is arbitrarily close to . In particular, we show the density of Chern slopes in the pathological Bogomolov–Miyaoka–Yau interval for any given . Moreover, we prove that for there exist surfaces as above with , 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 for any given .
"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