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Néron–Severi Lie Algebra, Autoequivalences of the Derived Category, and Monodromy
Moscow Mathematical Journal. 2022. Vol. 22. No. 4. P. 705–739.
Lunts V.
Let X be a smooth complex projective variety. The group of autoequivalences of the derived category of X acts naturally on its singular cohomology H(X; Q) and we denote by Geq(X) GL(H(X; Q)) its image. Let Geq(X) GL(H(X; Q) be its Zariski closure. We study the relation of the Lie algebra LieGeq(X) and the Neron{Severi Lie
algebra gNS(X) End(H(X; Q)) in case X has trivial canonical line bundle.
At the same time for mirror symmetric families of (weakly) Calabi-Yau varieties we consider a conjecture of Kontsevich on the relation between the monodromy of one family and the group Geq(X) for a very
general member X of the other family.
Publication based on the results of:
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