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2 results

ON THE EXISTENCE OF A GLOBAL NEIGHBOURHOOD
Part of
TOM COATES, HIROSHI IRITANI
Journal: Glasgow Mathematical Journal / Volume 58 / Issue 3 / September 2016
Published online by Cambridge University Press: 21 July 2015, pp. 717-726
Print publication: September 2016
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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.

A mirror theorem for toric stacks
Part of
Tom Coates, Alessio Corti, Hiroshi Iritani, Hsian-Hua Tseng
Journal: Compositio Mathematica / Volume 151 / Issue 10 / October 2015
Published online by Cambridge University Press: 01 June 2015, pp. 1878-1912
Print publication: October 2015
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We prove a Givental-style mirror theorem for toric Deligne–Mumford stacks ${\mathcal{X}}$. This determines the genus-zero Gromov–Witten invariants of ${\mathcal{X}}$ in terms of an explicit hypergeometric function, called the $I$-function, that takes values in the Chen–Ruan orbifold cohomology of ${\mathcal{X}}$.