Let E be a toric fibration arising from symplectic reduction of a direct sum of complex line bundles over (almost) Kähler base B. Then each torus-fixed point of the toric manifold fiber defines a section of the fibration. Let Labe convex line bundles over B, Aa smooth divisors of B arising as the zero loci of generic sections of La , and a particular fixed-point section of E. Further assume the {Aa} to be mutually disjoint. The manifold is a new manifold with tautological line bundles over new projective spaces in the geometry, where previously there was a simpler vector bundle in the given local geometry (Section 1.5). Thus, we compute genus-0 Gromov-Witten invariants of in terms of genus-0 Gromov-Witten invariants of B and of {Aa}, the matrix used for the symplectic reduction description of the fiber of the toric fibration E→B, and the restriction maps . The proofs utilize the fixed-point localization technique describing the geometry of and its genus-0 Gromov-Witten theory, as well as the Quantum Lefschetz theorem relating the genus-0 Gromov-Witten theory of A with that of B.
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![\"\"](\"Edit_170b9ffb-960a-4baa-8267-393b7b206331.bmp\")
a particular fixed-point section of E. Further assume the {Aa} to be mutually disjoint. The manifold ![\"\"](\"Edit_04f8d5f6-a5b4-4ea5-a023-053c02222681.bmp\")
is a new manifold with tautological line bundles over new projective spaces in the geometry, where previously there was a simpler vector bundle in the given local geometry (Section 1.5). Thus, we compute genus-0 Gromov-Witten invariants of ![\"\"](\"Edit_cf4322b0-67d7-4ef3-b3e3-71c6d2734535.bmp\")
in terms of genus-0 Gromov-Witten invariants of B and of ![\"\"](\"Edit_d01212c2-e85d-4dee-850a-7f59761730c1.bmp\")
. The proofs utilize the fixed-point localization technique describing the geometry of ![\"\"](\"Edit_8f4a28a8-4e6c-4586-97c6-513238e4b3e8.bmp\")
and its genus-0 Gromov-Witten theory, as well as the Quantum Lefschetz theorem relating the genus-0 Gromov-Witten theory of A with that of B.
