| 概要 | Spherical twists are certain autoequivalences of the
derived category D(X) of an algebraic variety X. Each such
twist is defined by a functor D(Z) -> D(X), where Z
is some other variety. In geometrical case, this functor
is defined by a subvariety of X flatly fibered over Z.
In this talk I will first give a short introduction
to these twists, recalling ther definition and construction.
Then I will explain sufficient criteria for several
such twists to define a categorical action of the braid
group on D(X). I will first give these in general
form, which applies to the twists defined by any abstract
functors. Then I give a geometrical interpretation for
the case when the twists are defined by fibered subvarieties
of X as above. This is joint work with Rina Anno (UPitt). |