On the Existence of a Global Neighbourhood

Abstract

Suppose that a complex manifold M is locally embedded into a higher-dimensional neighbourhood as a submanifold. We show that, if the local neighbourhood germs are compatible in a suitable sense, then they glue together to give a global neighbourhood of M. As an application, we prove a global version of Hertling--Manin's unfolding theorem for germs of TEP structures; this has applications in the study of quantum cohomology.

9 pages

References in corpus (2)

• Technical details on Kuranishi structure and virtual fundamental chain
• A construction of Frobenius manifolds with logarithmic poles and applications

Cited by in corpus (2)

• Gromov-Witten Invariants of Local P^2 and Modular Forms
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