# Hebrew University topology and geometry seminar

December 16, 2015

1100-1235

Ross building, Seminar Room 70A

## Yochay Jerby

*Hebrew University of Jerusalem
*

##
Exceptional collections on toric Fano manifolds and the Landau-Ginzburg equations

**Abstract:**
For a toric Fano manifold $X$ denote by $Crit(X) \subset (\mathbb{C}^{\ast})^n$ the solution scheme of the Landau-Ginzburg system of equations of $X$.
Examples of toric Fano manifolds with $rk(Pic(X)) \leq 3$ which admit full strongly exceptional collections of line bundles were recently found by various authors.
For these examples we construct a map $E : Crit(X) \rightarrow Pic(X)$ whose image $\mathcal{E}=\left \{ E(z) \vert z \in Crit(X) \right \}$ is a full strongly exceptional
collection satisfying the M-aligned property. That is, under this map, the groups $Hom(E(z),E(w))$ for $z,w \in Crit(X)$ are naturally related to the structure of the monodromy
group acting on $Crit(X)$.