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A volume maximizing canonical surface in 3-space

Ingrid Bauer·Fabrizio Catanese
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Abstract

Answering a question posed by Enriques, we construct a minimal smooth algebraic surface $S$ of general type over the complex numbers with $K^2 = 45$ and $p_g = 4$, and with birational canonical map. Our surface is a regular (q=0) ball quotient which is an etale quotient of a Hirzebruch covering of the plane. The canonical system $|K_S|$ has a fixed part and the degree of the canonical image is 19.

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Ingrid Bauer, Fabrizio Catanese. 2006-08-01. A volume maximizing canonical surface in 3-space. https://arxiv.org/abs/math/0608020

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