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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DOI:
https://doi.org/10.1090/S0273-0979-1992-00244-6

Article copyright:
© Copyright 1992
American Mathematical Society