European Journal of Mathematics

, Volume 5, Issue 3, pp 771–797 | Cite as

Perverse schobers on Riemann surfaces: constructions and examples

  • Will DonovanEmail author
Research Article


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.


Perverse sheaves Perverse schobers Derived categories Riemann surfaces Geometric invariant theory Flops Mirror symmetry 

Mathematics Subject Classification

14F05 14E05 14J33 14L24 18E30 



I am grateful to Mikhail Kapranov for inspiring conversations. I thank Alexey Bondal, Yukari Ito, Alastair King, Sven Meinhardt, Ed Segal, and Michael Wemyss for useful discussions, and Jacopo Stoppa and Barbara Fantechi for their hospitality and interest in my work at SISSA, Trieste. I am grateful to an anonymous referee, and to Pierre Schapira, for helpful comments. Finally, I thank the organizers of the 2016 Easter Island workshop on algebraic geometry for the opportunity to attend.


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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Yau Mathematical Sciences CenterTsinghua UniversityHaidian District, BeijingChina

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