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2009

Gromov-- Witten Invariants of Toric Fibrations

Brown, Jeffrey

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We prove a conjecture of Artur Elezi in a generalized form suggested by Givental.

Namely, our main result relates genus-0 Gromov--Witten invariants of a bundle space with such invariants of the base, provided that the fiber is a toric manifold.
When the base is the point, a new proof of mirror theorems by A.
Givental and by H.

Gromov-- Witten Invariants of Toric Fibrations · Around

Built on

M. Kontsevich. Enumeration of rational curves via tori actions
1995
Earlier work this paper cites.
A. Givental. A mirror theorem for toric complete intersections
1998
Earlier work this paper cites.
T. Graber, R. Pandharipande. Localization of virtual classes
1999
Earlier work this paper cites.

Similar

S. Barannikov. Quantum Periods- I. Semi- infinite variations of Hodge structures
2001
Cited alongside, same era.
A. Givental. Symplectic geometry of Frobenius structures
2004
Cited alongside, same era.
A. Elezi. A mirror conjecture for projective bundles
2005
Cited alongside, same era.
J. Brown, T. Coates, A. Givental, H.-H. Tseng. Virasoro constraints for toric fibrations
Cited in the paper.

Then

A. Givental. Gromov–Witten invariants of symplectic quotients
2006
Later among the works it cites.
T. Coates, A. Givental. Quantum Riemann-Roch, Lefschetz and Serre
2007
Later among the works it cites.
H. Iritani. Quantum D- modules and generalized mirror transformations
2008
Later among the works it cites.

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