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:M →D ⊑C
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 |
本文献已被 SpringerLink 等数据库收录! |
|