## Duke Mathematical Journal

Published by Duke University Press since its inception in 1935, the *Duke Mathematical Journal* is one of the world's leading mathematical journals. *DMJ* emphasizes the most active and influential areas of current mathematics. Advance publication of articles online is available.

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**ISSN:**0012-7094 (print), 1547-7398 (electronic)**Publisher:**Duke University Press**Discipline(s):**Mathematics**Full text available in Euclid:**1935--**Access:**By subscription only**Euclid URL:**http://projecteuclid.org/dmj

### Featured bibliometrics

*MR Citation Database* MCQ (2015): 2.29

*JCR* (2015) Impact Factor: 2.350

*JCR* (2015) Five-year Impact Factor: 2.337

*JCR* (2015) Ranking: 9/312 (Mathematics)

Article Influence: 3.899

Eigenfactor: Duke Mathematical Journal

SJR/SCImago Journal Rank (2015): 5.675

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### Featured article

* *Chern slopes of surfaces of general type in positive characteristic

##### Abstract

Let $\mathbf{k}$ be an algebraically closed field of characteristic $p>0$, and let $C$ be a nonsingular projective curve over $\mathbf{k}$. We prove that for any real number $x\ge 2$, there are minimal surfaces of general type $X$ over $\mathbf{k}$ such that (a) ${c}_{1}^{2}\left(X\right)>0$, ${c}_{2}\left(X\right)>0$, (b) ${\pi}_{1}^{\stackrel{\xb4}{e}t}\left(X\right)\simeq {\pi}_{1}^{\stackrel{\xb4}{e}t}\left(C\right)$, and (c) ${c}_{1}^{2}\left(X\right)/{c}_{2}\left(X\right)$ is arbitrarily close to $x$. In particular, we show the density of Chern slopes in the pathological Bogomolov–Miyaoka–Yau interval $(3,\infty )$ for any given $p$. Moreover, we prove that for $C={\mathbb{P}}^{1}$ there exist surfaces $X$ as above with ${H}^{1}(X,{\mathcal{O}}_{X})=0$, 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 $[2,\infty )$ for any given $p$.