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

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.

82 pages, in version 2: some typos corrected and references added

References in corpus (3)

• A Mathematical Theory of the Gauged Linear Sigma Model
• Landau-Ginzburg Mirror Symmetry Conjecture
• Asymptotic Expansion and the LG/(Fano, General Type) Correspondence

Cited by in corpus (2)

• A mirror theorem for genus two Gromov-Witten invariants of quintic threefolds
• D-brane central charge and Landau-Ginzburg orbifolds