Quantum cohomology of projective bundles

2023/07/07 by Iritani, Hiroshi, Koto, Yuki
#Algebraic Geometry (math.AG) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2307.03696

Abstract

We construct an I-function of the projective bundle P(V) associated with a not necessarily split vector bundle V→ B as a Fourier transform of the S¹-equivariant J-function of the total space of V and show that it lies on the Givental Lagrangian cone of P(V). Using this result, we show that the quantum cohomology D-module of P(V) splits into the direct sum of the quantum cohomology D-modules of the base space B. This has applications to the semisimplicity of big quantum cohomology.

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