2019/01/25 by Alessio Corti, Corti, Alessio, Giulia Gugiatti +1 · 1 citation
Computer Science · Mathematics · #14D07 #14Exx #14J33 #33Cxx #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Coding theory and cryptography #FOS: Mathematics #Polynomial and algebraic computation #math.AG #msc:14D07 #msc:14Exx #msc:14J33 #msc:33Cxx
paper · pdf · doi:10.48550/arxiv.1901.09026
28 pages
openalex publication_date 2019/01/25 · arxiv created 2019/07/23 · arxiv updated 2019/07/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For all k>0 integer, we consider the regularised I-function of the family of del Pezzo surfaces of degree 8k+4 in P(2,2k+1,2k+1, 4k+1), first constructed by Johnson and Kollár. We show that this function, which is of hypergeometric type, is a period of an explicit pencil of curves. Thus the pencil is a candidate LG mirror of the family of del Pezzo surfaces. The main feature of these surfaces, which makes the mirror construction especially interesting, is that the anticanonical system is empty: because of this, our mirrors are not covered by any other construction known to us. We discuss connections to the work of Beukers, Cohen and Mellit on hypergeometric functions.