Commentarii Mathematici Helvetici

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Volume 83, Issue 2, 2008, pp. 387–406
DOI: 10.4171/CMH/129

Published online: 2008-06-30

A volume maximizing canonical surface in 3-space

Ingrid Bauer[1] and Fabrizio Catanese[2]

(1) Universit├Ąt Bayreuth, Germany
(2) Universit├Ąt Bayreuth, Germany

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. The canonical system |KS| has a fixed part and the degree of the canonical image is 19. The surface we construct is rigid, S is indeed a ball quotient. It is obtained as an Abelian covering of the plane branched over an arrangement of lines already considered by Hirzebruch, and it is the first such example which is regular (q = 0).

Keywords: Regular ball quotients, configurations of lines

Bauer Ingrid, Catanese Fabrizio: A volume maximizing canonical surface in 3-space. Comment. Math. Helv. 83 (2008), 387-406. doi: 10.4171/CMH/129