Local moduli spaces in analytic geometry
A graded complex space is a graded \({\mathbb{C}}\)-ringed space (X,\({\mathcal O})\), \({\mathcal O}=\oplus_{k\geq 0}{\mathcal O}_ k\), such that: (X,\({\mathcal O}_ 0)\) is a complex space, \({\mathcal O}\) is an \({\mathcal O}_ 0\)-algebra of finite presentation and each \({\mathcal O}_ k\) is coherent over \({\mathcal O}_ 0\). A very general existence theorem for local moduli spaces in the context of graded complex spaces is presentated in this first paper (to be continued in the following review). This result includes as special cases the existence of local moduli for compact complex spaces, isolated singularities, coherent analytic sheaves with compact supports or isolated singularities, principal bundles over compact complex spaces, as well as the existence of the Douady spaces.
scientific article; zbMATH DE number 4032082
scientific article