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

Written by semaphores | Published 2024/06/10
Tech Story Tags: mirror-theorem | non-split-toric-bundles | toric-bundles | brown's-i-function | givental-lagrangian-cones | gromov-witten-theory | fiber | riemann-roch-theorem

TLDRThis research paper develops a new method (I-functions) for understanding mirror symmetry in complex spaces called non-split toric bundles.via the TL;DR App

Author:

(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.


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Published by HackerNoon on 2024/06/10