Mathematics – Algebraic Geometry
Scientific paper
2011-06-23
Mathematics
Algebraic Geometry
48 pages, 1 figure, part of the author's PhD thesis
Scientific paper
We define a period map for classical Campedelli surfaces, using a covering trick as in the case of Enriques surfaces: the period map is shown to come from a family of Enriques surfaces, obtained as quotients of the Campedelli surface by an involution. The period map realises an isomorphism between a projective variety obtained by invariant theory, and the Baily-Borel compactification of an arithmetic quotient, in the same fashion as in the work of Matsumoto, Sasaki and Yoshida. The result is proved from scratch using traditional methods. As another consequence we determine properties of the monodromy of Campedelli surfaces with a choice of double cover.
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