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Licensed Unlicensed Requires Authentication Published by De Gruyter August 14, 2019

Mukai’s program (reconstructing a K3 surface from a curve) via wall-crossing

  • Soheyla Feyzbakhsh
An erratum for this article can be found here: https://doi.org/10.1515/crelle-2020-0037

Abstract

Let C be a curve of genus g=11 or g13 on a K3 surface whose Picard group is generated by the curve class [C]. We use wall-crossing with respect to Bridgeland stability conditions to generalise Mukai’s program to this situation: we show how to reconstruct the K3 surface containing the curve C as a Fourier–Mukai transform of a Brill–Noether locus of vector bundles on C.

Award Identifier / Grant number: WallXBirGeom 337039

Funding statement: The author was supported by the ERC starting grant WallXBirGeom 337039.

Acknowledgements

I would like to thank Arend Bayer for many useful discussions. I am grateful for comments by Benjamin Bakker, Gavril Farkas, Chunyi Li and Bach Tran. I would also like to thank the referees for their careful reading of the paper, and for many useful suggestions.

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Received: 2017-10-27
Revised: 2019-01-24
Published Online: 2019-08-14
Published in Print: 2020-08-01

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