6 papers
Notes on the decomposition theorem for blowups
Hiroshi Iritani
We discuss arithmetic and Hodge-theoretic properties of the isomorphisms appearing in the decomposition theorem for quantum cohomology of blowups. These properties underpin the app…
Quantum cohomology of projective bundles
Hiroshi Iritani, Yuki Koto
We construct an I-function of the projective bundle P(V) associated with a not necessarily split vector bundle V\to B as a Fourier transform of the S^1-equivariant J-function of th…
Fourier analysis of equivariant quantum cohomology
Hiroshi Iritani
Equivariant quantum cohomology possesses the structure of a difference module by shift operators (Seidel representation) of equivariant parameters. Teleman's conjecture suggests th…
Quantum cohomology of blowups
Hiroshi Iritani
We prove a decomposition theorem of the quantum cohomology D-module of the blowup of a smooth projective variety X along a smooth subvariety Z. The main tools we use are shift oper…
Revisiting Gamma conjecture I: counterexamples and modifications
Sergey Galkin, Jianxun Hu, Hiroshi Iritani +3
We continue investigation of asymptotics of quantum differential equation for Fano manifolds, with a special regard to Gamma conjecture I and its underlying Conjecture $\mathcal{O}…
Mirror symmetric Gamma conjecture for Fano and Calabi-Yau manifolds
Hiroshi Iritani
The mirror symmetric Gamma conjecture roughly speaking says that the Gamma class of a manifold determines the asymptotics of (exponential) periods of the mirror. We recast the meth…