Mirrors of the Johnson-Kollár series
HARVARD-MIT ALGEBRAIC GEOMETRY
Giulia Gugiatti - Imperial College
I will construct LG mirrors for the Johnson-Kollár series of anticanonical del Pezzo surfaces in weighted projective 3-spaces. The main feature of these surfaces is that their anticanonical linear system is empty. Thus they fall outside of the range of the known mirror constructions. For each of these surfaces, the LG mirror is a pencil of hyperelliptic curves. I will exhibit the regularised I-function of the surface as a period of the pencil and I will sketch how to construct the pencil starting from a work of Beukers, Cohen, and Mellit on finite hypergeometric functions. This is joint work with Alessio Corti.