ON THE QUANTUM COHOMOLOGY RINGS OF GENERAL TYPE PROJECTIVE HYPERSURFACES AND GENERALIZED MIRROR TRANSFORMATION

DOI10.1142/S0217751X00000707zbMath0952.14037arXivhep-th/9811124MaRDI QIDQ4507760

Masao Jinzenji

Publication date: 8 October 2000

Published in: International Journal of Modern Physics A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-th/9811124

zbMATH Keywords

mirror transformationhypersurfaceGromov-Witten invariantsSchur polynomialsCalabi-Yau hypersurfacequantum cohomology ring

Mathematics Subject Classification ID

Calabi-Yau manifolds (algebro-geometric aspects) (14J32) Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) (14N35) Hypersurfaces and algebraic geometry (14J70)

Related Items (5)

Geometrical proof of generalized mirror transformation of projective hypersurfaces ⋮ Mirror map as generating function of intersection numbers: toric manifolds with two Kähler forms ⋮ Towards mirror symmetry for varieties of general type ⋮ Direct proof of the mirror theorem for projective hypersurfaces up to degree 3 rational curves ⋮ Moduli space of quasimaps from \(\mathbb{P}^1\) with two marked points to \(\mathbb{P}(1,1,1,3)\) and \(j\)-invariant

Cites Work

• A pair of Calabi-Yau manifolds as an exactly soluble superconformal theory.
• Summing the instantons: Quantum cohomology and mirror symmetry in toric varieties
• Mirror manifolds in higher dimension
• Gromov-Witten classes, quantum cohomology, and enumerative geometry
• CALCULATION OF GROMOV-WITTEN INVARIANTS FOR CP³, CP⁴AND Gr(2, 4)
• Construction of Free Energy of Calabi–Yau Manifold Embedded in CP^N-1 via Torus Actions
• On quantum cohomology rings for hypersurfaces in CPN−1
• Equivariant Gromov - Witten Invariants

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