2020/09/19 by Valery A. Lunts, Lunts, Valery
Mathematics · Pharmacology, Toxicology and Pharmaceutics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Alkaloids: synthesis and pharmacology
paper · pdf · doi:10.48550/arxiv.2009.09262
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) the Zariski closure of its image in Gl(H(X, Q)). We study the relation of the Lie algebra LieGeq(X) and the Neron-Severi Lie algebra gNS(X) 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.