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The moduli of substructures of a compact complex space |
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| Authors: | Peter M. Schuster |
| Affiliation: | Mathematisches Institut der Universität, Theresienstr. 39, 80333 München, Germany |
| Abstract: | We construct a space  of fine moduli for the substructures of an arbitrary compact complex space  . A substructure  of  is given by a subalgebra  of the structure sheaf  with the additional feature that  is also a complex space;  and  are called equivalent if and only if  and  are isomorphic as subalgebras of  . Since substructures are quotients, it is only natural to start with the fine moduli space |
| Keywords: | Moduli spaces substructures subalgebras quotients |
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of all complex-analytic quotients of 
. In order to obtain a representable moduli functor of substructures, we are forced to concentrate on families of quotients which satisfy some flatness condition for relative differential modules of higher order. Considering the corresponding flatification of 
, we realize that its open subset 
consisting of all substructures turns out to be a complex space which has the required universal property.