Article citationsMore>>

Givental, A. (1998) A Mirror Theorem for Toric Complete Intersections. In: Kashiwara, M., Matsuo, A., Saito, K. and Satake, I., Eds., Topological Field Theory, Primitive Forms and Related Topics. Progress in Mathematics, Birkhäuser, Boston, MA, 141-175.
https://doi.org/10.1007/978-1-4612-0705-4_5

has been cited by the following article:

• TITLE: Convolution Integrals and a Mirror Theorem from Toric Fiber Geometry

  AUTHORS: Jeff Brown

  KEYWORDS: Gromov-Witten Invariant, Quantum Cohomology, Fixed-Point Localization, Birational Geometry

  JOURNAL NAME: Advances in Pure Mathematics, Vol.9 No.9, September 16, 2019

  ABSTRACT: 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 La be 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.