Toric varieties arising from polygon dissections

A dissection of a polygon is obtained by drawing diagonals such that no two diagonals intersect in their interiors. In this talk, we define a toric variety and a rooted tree associated with a polygon dissection. The toric varieties arising from polygon dissections are Fano generalized Bott manifolds and classified up to isomorphism in terms of the associated rooted trees. We also discuss the relationship with torus orbit closures in flag varieties for the toric varieties arising from polygon dissections.