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The Slope of Surfaces with Albanese Dimension One

Published online by Cambridge University Press:  28 May 2018

STEFANO VIDUSSI
STEFANO VIDUSSI*
Affiliation:
Department of Mathematics, University of California, Riverside, CA 92521, U.S.A. e-mail: svidussi@ucr.edu
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Abstract

Mendes Lopes and Pardini showed that minimal general type surfaces of Albanese dimension one have slopes K2/χ dense in the interval [2,8]. This result was completed to cover the admissible interval [2,9] by Roulleau and Urzua, who proved that surfaces with fundamental group equal to that of any curve of genus g ≥ 1 (in particular, having Albanese dimension one) give a set of slopes dense in [6,9]. In this note we provide a second construction that complements that of Mendes Lopes–Pardini, to recast a dense set of slopes in [8,9] for surfaces of Albanese dimension one. These surfaces arise as ramified double coverings of cyclic covers of the Cartwright–Steger surface.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 167 , Issue 2 , September 2019 , pp. 355 - 360
Copyright
Copyright © Cambridge Philosophical Society 2018 

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