2017/01/02 by Todor Milanov, Milanov, Todor · 2 citations
Mathematics · Physics and Astronomy · #14D07 #14N35 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.1701.00393
openalex publication_date 2017/01/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The main goal of this paper is to introduce the notion of a primitive form for a generic family of Hurwitz covers of ℙ1 with a fixed ramification profile over infinity. We prove that primitive forms are in one-to-one correspondence with semi-simple Frobenius structures on the base of the family. Furthermore, we introduce the notion of a polynomial primitive form and show that the corresponding class of Frobenius manifolds contains the Hurwitz Frobenius manifolds of Dubrovin. Finally, we apply our theory to investigate the relation between the Eynard--Orantin recursion and Frobenius manifolds.