Twisted cubics on cubic fourfolds and stability conditions

We give an interpretation of the Fano variety of lines on a cubic fourfold and of the hyperkähler eightfold, constructed by Lehn, Lehn, Sorger and van Straten from twisted cubic curves in a cubic fourfold not containing a plane, as moduli spaces of Bridgeland stable objects in the Kuznetsov component. As a consequence, we obtain the identification of the period point of the LLSvS eightfold with that of the Fano variety. We discuss the derived Torelli theorem for cubic fourfolds. © Foundation Compositio Mathematica 2023. This article is distributed with Open Access under the terms of the Creative Commons Attribution Non-Commercial License, which permits non-commercial reuse, distribution, and reproduction in any medium, provided that the original work is properly cited. For commercial re-use, please contact the Foundation Compositio Mathematica.