The coherent-constructible correspondence for toric projective bundles

Abstract: This talk is about the coherent-constructible correspondence (CCC). CCC is a version of homological mirror symmetry for toric varieties. It equates the derived category of coherent sheaves on a toric variety and the category of constructible sheaves on a torus that satisfy some condition on singular support. Recently, Harder-Katzarkov conjectured that there should be a version of CCC for toric fiber bundles and they proved their conjecture for $\mathbb{P}^1$-bundles. I will explain how we can prove (half of) their conjecture for $\mathbb{P}^n$-bundles. If time permits, I will give a more precise version of the conjecture for arbitrary toric fiber bundles.

algebraic geometrysymplectic geometry

Audience: researchers in the topic

M-seminar