tt*-geometry in quantum cohomology

2009/06/06 by Hiroshi Iritani, Iritani, Hiroshi · 1 citation
Mathematics · #14N35 #32G20 #32G34 #34M55 #53D45 #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #math.AG #math.DG #msc:14N35 #msc:32G20 #msc:32G34 #msc:34M55 #msc:53D45

paper · pdf · doi:10.48550/arxiv.0906.1307

34 pages. This paper is a revision of the real structure part of the preprint arXiv:0712.2204

arxiv created 2009/06/06 · openalex publication_date 2009/06/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study possible real structures in the space of solutions to the quantum differential equation. We show that, under mild conditions, a real structure in orbifold quantum cohomology yields a pure and polarized tt^*-geometry near the large radius limit. We compute an example of P¹ which is pure and polarized over the whole Kaehler moduli space H²(P¹,C^*).

Citations

• Real and integral structures in quantum cohomology I: toric orbifolds

Cited by

• Schrödinger equations, deformation theory and tt^*-geometry

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