Gamma conjecture via mirror symmetry

The asymptotic behaviour of solutions to the quantum differential equation of a Fano manifold F defines a characteristic class A_F of F, called the principal asymptotic class. Gamma conjecture of Vasily Golyshev and the present authors claims that the principal asymptotic class A_F equals the Gamma...

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Bibliographic Details
Published inarXiv.org
Main Authors Galkin, Sergey, Iritani, Hiroshi
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 25.07.2018
Subjects
Asymptotic properties
Differential equations
Hyperplanes
Intersections
Mathematics - Algebraic Geometry
Mathematics - Classical Analysis and ODEs
Mathematics - Number Theory
Mathematics - Symplectic Geometry
Polynomials
Symmetry
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Summary:The asymptotic behaviour of solutions to the quantum differential equation of a Fano manifold F defines a characteristic class A_F of F, called the principal asymptotic class. Gamma conjecture of Vasily Golyshev and the present authors claims that the principal asymptotic class A_F equals the Gamma class G_F associated to Euler's \(\Gamma\)-function. We illustrate in the case of toric varieties, toric complete intersections and Grassmannians how this conjecture follows from mirror symmetry. We also prove that Gamma conjecture is compatible with taking hyperplane sections, and give a heuristic argument how the mirror oscillatory integral and the Gamma class for the projective space arise from the polynomial loop space.
Bibliography:SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
content type line 50
ISSN:2331-8422
DOI:10.48550/arxiv.1508.00719