Mirror symmetric Gamma conjecture for Fano and Calabi-Yau manifolds

Author:

Hiroshi Iritani

Keyword:

Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG), High Energy Physics - Theory (hep-th), Symplectic Geometry (math.SG)

journal:

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date:

2023-07-28 16:00:00

Abstract

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 method in [Iri11] in a more general context and show that the mirror symmetric Gamma conjecture for a Fano manifold F implies, via Laplace transformation, that for the total space K_F of the canonical bundle or for anticanonical sections in F. More generally, we discuss the mirror symmetric Gamma conjecture for the total space of a sum of anti-nef line bundles over F or for nef complete intersections in F.