论文标题
Neron-Severi Lie代数，派生类别的自动等效性和单片
Neron-Severi Lie algebra, autoequivalences of the derived category, and monodromy
论文作者
论文摘要
令X为平滑的复杂投影品种。 X的派生类别的自动等量组自然作用于其奇异的共同体H（X，Q），我们用GEQ（x）表示其图像的Zariski在GL（H（H（H（X，Q）））中闭合。我们研究Lie代数Liegeq（X）和Neron-Severi Lie代数GNS（X）的关系，以防X具有琐碎的规范线束。同时，（弱）calabi-yau品种的镜像对称家族，我们考虑了Kontsevich对一个家族的单元与GEQ组（X）之间的关系的猜想。
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.
