Perverse schobers on Riemann surfaces: constructions and examples

This note studies perverse sheaves of categories, or schobers, on Riemann surfaces, following ideas of Kapranov and Schechtman (Perverse schobers, arXiv:1411.2772, 2014). For certain wall crossings in geometric invariant theory, we construct a schober on the complex plane, singular at each imaginary integer. We use this to obtain schobers for standard flops: in the threefold case, we relate these to a further schober on a partial compactification of a stringy Kähler moduli space, and suggest an application to mirror symmetry.