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

10 Jun 2024


(1) Yuki Koto

3. Toric bundles

In this section we introduce toric bundles. We first review toric varieties, and then define toric bundles by doing the construction of toric varieties in a relative setting. Note that they include toric bundles appearing in [5] [21]. We then investigate geometric structures of toric bundles: T-equivariant cohomology ring (3.2), effective curves (3.3), T-fixed loci and one-dimensional orbits (3.4).

As explained in Section 1, mirror theorems for split toric bundles [5] and (non-split) projective bundles [21] are already known. We will prove a mirror theorem for (non-split) toric bundles (Theorem 6.1).

This paper is available on arxiv under CC 4.0 license.