Gromov-Witten Theory of Quotient of Fermat Calabi-Yau varieties

2016/05/28 by Hiroshi Iritani, Todor Milanov, Iritani, Hiroshi +5 · 1 citation
Mathematics · #14N35 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #FOS: Physical sciences #Geometry and complex manifolds #High Energy Physics - Theory (hep-th)

paper · pdf · doi:10.48550/arxiv.1605.08885

openalex publication_date 2016/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct a global B-model for weighted homogeneous polynomials based on K. Saito's theory of primitive forms. Our main motivation is to give a rigorous statement of the so called global mirror symmetry conjecture relating Gromov-Witten invariants and Fan--Jarvis--Ruan--Witten invariants. Furthermore, our construction allows us to generalize the notion of a quasi-modular form and holomorphic anomaly equations. Finally, we prove the global mirror symmetry conjecture for the Fermat polynomials.

Citations

• Landau-Ginzburg Mirror Symmetry Conjecture
• The Witten equation and its virtual fundamental cycle

Cited by

• A mirror theorem for genus two Gromov-Witten invariants of quintic threefolds

Related

• Landau-Ginzburg Mirror Symmetry Conjecture
• Gromov-Witten theory of elliptic orbifold P¹ and quasi-modular forms
• Refined Gromov-Witten invariants
• A Landau-Ginzburg/Calabi-Yau correspondence for the mirror quintic
• Global mirror symmetry for invertible simple elliptic singularities