Twisted cubics on cubic fourfolds and stability conditions

TL;DR

This paper interprets certain hyperkähler varieties associated with cubic fourfolds as moduli spaces of Bridgeland stable objects, providing new insights into their geometric and categorical properties.

Contribution

It offers a novel interpretation of the Fano variety and LLSvS eightfold as moduli spaces of stable objects in the Kuznetsov component, advancing the understanding of cubic fourfolds.

Findings

Reproves the categorical Torelli Theorem for cubic fourfolds

Identifies the period point of LLSvS eightfold with that of the Fano variety

Discusses derived Torelli Theorem for cubic fourfolds

Abstract

We give an interpretation of the Fano variety of lines on a cubic fourfold and of the hyperkahler eightfold, constructed by Lehn, Lehn, Sorger and van Straten from twisted cubic curves in a cubic fourfold non containing a plane, as moduli spaces of Bridgeland stable objects in the Kuznetsov component. As a consequence, we reprove the categorical version of Torelli Theorem for cubic fourfolds, we obtain the identification of the period point of LLSvS eightfold with that of the Fano variety, and we discuss derived Torelli Theorem for cubic fourfolds.