Author:
(1) Yuki Koto 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. This paper is available on arxiv under CC 4.0 license. Author: (1) Yuki Koto Author: Author: (1) Yuki Koto 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 Abstract and Intro Abstract and Intro Genus-zero Gromov-Witten Theory Genus-zero Gromov-Witten Theory Toric Bundles Toric Bundles Lagrangian cones of Toric bundles Lagrangian cones of Toric bundles Mirror theorem for a product of projectives bundles Mirror theorem for a product of projectives bundles Mirror Theorem for Toric Bundles Mirror Theorem for Toric Bundles Appendix A. Equivariant Fourier Transformation and References 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. Gromov-Witten invariant and its variants 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. Quantum Riemann-Roch theorem and twisted theory. This paper is available on arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. available on arxiv

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A Mirror Theorem for Non-split Toric Bundles: Lagrangian Cones of Toric Bundles

A Mirror Theorem for Non-split Toric Bundles: Mirror Theorem for a Product of Projectives Bundle

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A Mirror Theorem for Non-split Toric Bundles: Genus-zero Gromov-Witten Theory

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A Mirror Theorem for Non-split Toric Bundles: Abstract and Intro

A Mirror Theorem for Non-split Toric Bundles: Abstract and Intro

A Mirror Theorem for Non-split Toric Bundles: Toric Bundles

A Mirror Theorem for Non-split Toric Bundles: Appendix a and References

A Mirror Theorem for Non-split Toric Bundles: Mirror Theorem for Toric Bundles

A Mirror Theorem for Non-split Toric Bundles: Abstract and Intro

A Mirror Theorem for Non-split Toric Bundles: Abstract and Intro

A Mirror Theorem for Non-split Toric Bundles: Toric Bundles

A Mirror Theorem for Non-split Toric Bundles: Appendix a and References

A Mirror Theorem for Non-split Toric Bundles: Mirror Theorem for Toric Bundles

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