Abstract

Let (ℳ, B, ϖ) be a complex analytic family of compact complex manifolds where B is a domain of ℂ. Then the infinitesimal deformation dMt/dt of M t = ϖ−1 (t) is an element of H1(M t , Θ t ). Consequently, given a compact complex manifold M, if (ℳ, B, ϖ) with 0 ∈ B ⊂ ℂ is a complex analytic family such that ϖ−1(0) = M, (dM t /dt)t=0 ∈ H1 (M, Θ), where Θ is the sheaf of germs of holomorphic vector fields over M. Thus, if there is a complex analytic family (ℳ, B, ϖ) with ϖ−1(0) = M, the corresponding element θ = (dM t /dt) t=0 of H1 (M, Θ) is determined.KeywordsExact SequenceComplex ManifoldLocal ComplexCompact Complex ManifoldInfinitesimal DeformationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Full Text
Paper version not known

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.