Primitive Forms for Affine Cusp Polynomials

2012/11/06 by Yoshihisa Ishibashi, Ishibashi, Yoshihisa, Yuuki Shiraishi +3 · 2 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.1211.1128

openalex publication_date 2012/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We determine a primitive form for a universal unfolding of an affine cusp polynomial. Moreover, we prove that the resulting Frobenius manifold is isomorphic to the one constructed from the Gromov-Witten theory for an orbifold projective line with at most three orbifold points.

Citations

• Gromov--Witten invariants for mirror orbifolds of simple elliptic singularities
• Gromov-Witten theory of orbicurves, the space of tri-polynomials and Symplectic Field Theory of Seifert fibrations

Cited by

• Dubrovin duality for open Hurwitz flat F-manifolds
• Frobenius manifold for the nodal quiver

Related

• On the Frobenius Manifolds for Cusp Singularities
• Mirror symmetry for a cusp polynomial Landau-Ginzburg orbifold
• On Frobenius Manifolds from Gromov--Witten Theory of Orbifold Projective Lines with r orbifold points
• Unfoldings of meromorphic connections and a construction of Frobenius manifolds
• Primitive forms and Frobenius structures on the Hurwitz spaces