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A regularity theorem for deformations of a compact complex surface
Authors:Adam Harris
Institution:1. Department of Mathematics, State University of New York at Stony Brook, 11794, Stony Brook, New York
Abstract:Let ƒ:MDC n be a holomorphic family of compact, complex surfaces, which is locally trivial onD∖Z, for an analytic subsetZ. Conditions are found under which ƒ extends trivially toD, if the fibers of ƒ|D∖Z are either Hirzebruch surfaces (projective bundles overP 1), Hopf surfaces (elliptic bundles overP 1), hyperelliptic bundles, or any compact complex surface having one of these as minimal model under blowing-down. The results of this paper are motivated by the existence of non-Hausdorff moduli spaces in the deformation of complex structure for certain complex manifolds.
Keywords:Math Subject Classification" target="_blank">Math Subject Classification  14H15  32G05  32G13  32J15
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