Mirrors, Functoriality, and Derived Geometry

2017/08/09 by Yuri I. Manin, Manin, Yu. I.
Mathematics · #18D50 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1708.02849

openalex publication_date 2017/08/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this survey, I suggest to approach the problem of functorial properties of quantum cohomology by drawing lessons from several versions of Mirror duality involving deformation spaces.

Citations

• Towards motivic quantum cohomology of M_0,S
• Weak mirror symmetry of Lie algebras

Related

• Localized mirror functor for Lagrangian immersions, and homological mirror symmetry for P¹_a,b,c
• Classification problems and mirror duality
• Introduction to Duality
• Introduction to homological geometry: part II
• Mirror symmetry and quantum cohomology of projective bundles