Abstract: |
Due to Lowen, first order curved dg deformations of a curved dg category is classified by its second Hochschild cohomology. Keller provided a sufficient condition for a dg category to have the Morita deformation along a given Hochschild cocycle. In this talk, we show that, for a higher dimensional Calabi--Yau manifold, giving curved dg deformations of the category of perfect complexes is equivalent to giving its Morita deformations. We explain how it leads us to the construction of a natural isomorphism from the deformation functor of the Calabi--Yau manifold to that of the dg category of perfect complexes. As a consequence, we obtain geometrically a versal dg deformation of the dg category of perfect complexes. If time allows, we show the independence of such versal deformations in a certain sense from the choice of the initial Calabi--Yau manifold. This talk is based on the corrected version of arXiv:2111.11778v2, which I will upload as soon as possible. |