Perverse schobers on Riemann surfaces: constructions and examples

TL;DR

This paper explores the construction of perverse sheaves of categories, called schobers, on Riemann surfaces, with applications to wall crossings, flops, and potential implications for mirror symmetry.

Contribution

It introduces new constructions of schobers on the complex plane related to wall crossings and flops, linking them to moduli spaces and mirror symmetry.

Findings

Constructed schobers singular at imaginary integers

Related schobers to standard flops in 3-folds

Connected schobers to stringy Kähler moduli space

Abstract

This note studies perverse sheaves of categories, or schobers, on Riemann surfaces, following ideas of Kapranov and Schechtman. For certain wall crossings in geometric invariant theory, I construct a schober on the complex plane, singular at each imaginary integer. I use this to obtain schobers for standard flops: in the 3-fold case, I relate these to a further schober on a partial compactification of a stringy Kaehler moduli space, and suggest an application to mirror symmetry.