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Lifting of cohomology and unobstructedness of certain holomorphic maps


Author: Ziv Ran
Journal: Bull. Amer. Math. Soc. 26 (1992), 113-117
MSC (2000): Primary 32G05; Secondary 14D15, 32G13
DOI: https://doi.org/10.1090/S0273-0979-1992-00244-6
MathSciNet review: 1102754
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Abstract: Let f be a holomorphic mapping between compact complex manifolds. We give a criterion for f to have unobstructed deformations, i.e. for the local moduli space of f to be smooth: this says, roughly speaking, that the group of infinitesimal deformations of f, when viewed as a functor, itself satisfies a natural lifting property with respect to infinitesimal deformations. This lifting property is satisfied e.g. whenever the group in question admits a 'topological' or Hodge-theoretic interpretation, and we give a number of examples, mainly involving Calabi-Yau manifolds, where that is the case.


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Additional Information

DOI: https://doi.org/10.1090/S0273-0979-1992-00244-6
Article copyright: © Copyright 1992 American Mathematical Society