Uniruled surfaces of general type
type: Item
instance of: scholarly article
title: Uniruled surfaces of general type
zbMATH Open document ID: 1157.14023
author: Christian Liedtke
published in: Mathematische Zeitschrift
publication date: 2008-06-30T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/0608604
review text: The author studies surfaces \(S\) in positive characteristics arising from the following construction: Let \(C,F\) be two curves endowed with \(p\)-closed rational vector fields \(\delta_C,\delta_F\), take the quotient of \(C\times F\) by the resulting rational vector field \(\delta_C+\delta_F\), and let \(S\) be a resolution of singularities. This construction is used to show that surfaces with unusual cohomological properties exist in abundance. The author mainly concentrates on uniruled surfaces of general type in characteristic two. For example, it is shown that there are families of such surfaces with the same reduced Picard scheme, but with \(h^{1,0}\) or \(h^{0,1}\) arbitrarily large, and that there are unbounded families of such surfaces having a purely inseparable canonical map factoring over a rational surface, or having nontrivial global vector fields. Furthermore, the author constructs a surface of general type with \(\chi=1\) and \(c_1^2=14\), which violates the Bogomolov-Miyaoka-Yau inequality \(c_1^2\leq 9\chi\).
reviewed by: Stefan Schröer
Mathematics Subject Classification ID: 14J29
zbMATH DE Number: 5294688
zbMATH Keywords: Surfaces of general type
zbMATH Keywords: uniruled surfaces
MaRDI profile type: Publication
OpenAlex ID: W2134603718
arXiv ID: math/0608604
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DOI: 10.1007/S00209-007-0248-7
description: scientific article