On strongly exceptional sequences of line bundles on toric varieties.

A by now classical result of Beilinson states that the
bounded derived category of coherent sheaves over projective
space is generated by a finite set of line bundles, which form
a so-called strongly exceptional collection. It is quite natural
to ask whether this generalizes to the case of toric varieties,
and in fact this is the content of a conjecture which was first
stated by King. In this talk we give an overview on the state
of King's conjecture along with examples, including the toric
3-fanos, and we also present a counterexample.