A volume maximizing canonical surface in 3-space
Abstract
Answering a question posed by Enriques, we construct a minimal smooth algebraic surface S of general type over the complex numbers with K2 = 45 and pg = 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 |KS| has a fixed part and the degree of the canonical image is 19.
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