2015/09/30 by Rodrigo Codorniu, Giancarlo Urzúa
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraically closed field #Combinatorics #Field (mathematics) #Geometry and complex manifolds #Invertible matrix #Mathematical analysis #Mathematics #Pure mathematics #Scheme (mathematics) #Type (biology) #math.AG #math.NT
paper · pdf · doi:10.1215/00127094-3792596
published as Duke Math. J. 166, no. 5 (2017), 975-1004
openalex created_date 2016/06/24 · arxiv created 2016/12/06 · openalex publication_date 2016/12/15 · arxiv updated 2017/04/05 · openalex updated_date 2026/08/05
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 x≥2, 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.