tt*-geometry in quantum cohomology

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 P^1 which is pure and polarized over the whole Kaehler moduli space H^2(P^1,C^*).

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

References in corpus (6)

• An integral structure in quantum cohomology and mirror symmetry for toric orbifolds
• Geometry and Integrability of Topological-Antitopological Fusion
• Fourier-Laplace transform of a variation of polarized complex Hodge structure
• Mixed twistor structures
• Real and integral structures in quantum cohomology I: toric orbifolds
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Cited by in corpus (9)

• An integral structure in quantum cohomology and mirror symmetry for toric orbifolds
• Quantum Cohomology and Periods
• Good Wild Harmonic Bundles and Good Filtered Higgs Bundles
• Schrödinger equations, deformation theory and $t{t}^{\ast }$-geometry
• Nonlinear PDE aspects of the tt* equations of Cecotti and Vafa
• Logarithmic Frobenius manifolds, hypergeometric systems and quantum D-modules
• Non-commutative Hodge structures
• tt*-Geometry on the big phase space
• Limits of families of Brieskorn lattices and compactified classifying spaces