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

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

4. Lagrangian cones of toric bundles

These sheaves are endowed with T-actions, and all arrows are T-equivariant. By taking the moving parts we obtain the following exact sequence:

The moving part can be described as

On the other hand, we have

These computations give the desired formula.

By performing calculations similar to those in the previous proof, we can establish the following formulas.

Using the above lemmas, we can compute the contributions of the graphs of type (α, 1).

Proposition 4.15.

Proof. To begin with, we rewrite the left-hand side using the bijection Φ1 as follows:

By using Lemma 4.11, Lemma 4.12 and Lemma 4.13, we have

4.4. Contribution of the (α, 2)-type graphs. The contribution of the (α, 2)-type graphs can be computed as follows.