A mirror theorem for toric stacks

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 ${...

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Veröffentlicht in:	Compositio mathematica 2015-10, Vol.151 (10), p.1878-1912
Hauptverfasser:	Coates, Tom, Corti, Alessio, Iritani, Hiroshi, Tseng, Hsian-Hua
Format:	Artikel
Sprache:	eng
Schlagworte:	Hypergeometric functions Invariants Stacks Theorems Theoretical mathematics
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Zusammenfassung:	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 ${\mathcal{X}}$.
ISSN:	0010-437X 1570-5846
DOI:	10.1112/S0010437X15007356