We give a proof of the formality conjecture of Kaledin and Lehn: on a complex projective K3 surface, the differential graded (DG) algebra $\operatorname{RHom}^{\bullet }(F,F)$ is formal for any sheaf… Click to show full abstract
We give a proof of the formality conjecture of Kaledin and Lehn: on a complex projective K3 surface, the differential graded (DG) algebra $\operatorname{RHom}^{\bullet }(F,F)$ is formal for any sheaf $F$ polystable with respect to an ample line bundle. Our main tool is the uniqueness of the DG enhancement of the bounded derived category of coherent sheaves. We also extend the formality result to derived objects that are polystable with respect to a generic Bridgeland stability condition.
Keywords:
formality conjecture;
formality;
conjecture surfaces
Journal Title: Compositio Mathematica
Year Published: 2019
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Journal Title: Compositio Mathematica
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!