Connected components of moduli spaces. (English) Zbl 0621.14014

Let S be a minimal surface of general type over the field of complex numbers and let M(S) be the coarse moduli space of complex structures on the oriented topological 4-manifold S. The following theorem shows that the number \(\lambda\) (S) of connected components of M(S) can be arbitrarily large:
For each natural number k there exist minimal models \(S_ 1,...,S_ k\) of surfaces of general type such that \((a)\quad S_ i\) is simply connected \((i=1,...,k)\); \((b)\quad for\) \(i\neq j\), \(S_ i\) and \(S_ j\) are (orientedly) homeomorphic but not a deformation of each other.
Reviewer: V.Iliev


14D20 Algebraic moduli problems, moduli of vector bundles
14J10 Families, moduli, classification: algebraic theory
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