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The Slope of Surfaces with Albanese Dimension One



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.



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The Slope of Surfaces with Albanese Dimension One



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