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Perverse schobers on Riemann surfaces: constructions and examples

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Abstract

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.

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Acknowledgements

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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  1. Yau Mathematical Sciences Center, Tsinghua University, Haidian District, Beijing, 100084, China

    Will Donovan

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Correspondence to Will Donovan.

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The author is supported by the World Premier International Research Center Initiative (WPI Initiative), MEXT, Japan, and JSPS KAKENHI Grant Number JP16K17561.

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Donovan, W. Perverse schobers on Riemann surfaces: constructions and examples. European Journal of Mathematics 5, 771–797 (2019). https://doi.org/10.1007/s40879-018-00307-2

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