Deformations of complex structures on supermanifolds
The author defines what is meant by a deformation of a complex supermanifold, defines the analogue of the classical Kodaira-Spencer map, and states the natural generalizations of the Kodaira-Nirenberg-Spencer existence theorems for versal deformations. It is interesting to note that superprojective spaces \(({\mathbb{P}}^{1/4}\), for example) may admit no trivial deformations. This is in line with \textit{P. S. Green}'s example of a non-trivial supermanifold in Proc. Am. Math. Soc. 85, 587-590 (1982; Zbl 0509.58001).
natural generalizations of the Kodaira-Nirenberg-Spencer existence theorems for versal deformations
scientific article; zbMATH DE number 3935468