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Author:
(1) Yuki Koto
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Table of Links
Abstract and Intro
Genus-zero Gromov-Witten Theory
Toric Bundles
Lagrangian cones of Toric bundles
Mirror theorem for a product of projectives bundles
Mirror Theorem for Toric Bundles
Appendix A. Equivariant Fourier Transformation and References
2. Genus-zero Gromov-Witten theory
In this section, we briefly recall the (torus-equivariant/twisted) genus-zero Gromov-Witten theory. We will introduce Gromov-Witten invariants, Givental Lagrangian cones and the quantum Riemann-Roch theorem.
2.1. Gromov-Witten invariant and its variants. We recall the definition of Gromov-Witten invariant. We also introduce an torus-equivariant version and a twisted version of it.
2.3. Quantum Riemann-Roch theorem and twisted theory. We introduce quantum Riemann-Roch theorem [9, Corollary 4], which relates twisted Givental cones via some transcendental operators. We also explain relationships between the Gromow-Witten theory of a vector bundle (resp. a subvariety) and that of a base space (resp. an ambient space) in terms of twisted theories. Note that we will use the material in this subsection only in Section 5.
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This paper is available on arxiv under CC 4.0 license.
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