## FSU Topology Week

Title: Birational maps fixing a curve with a cusp

Speaker: Kyounghee Kim (Florida State University)

Abstract: An element of T-shaped root system $T(2,q,r)$ can be realized by a lift of a birational map on ${\bf P}^{q-1}$. One method for constructing such birational maps is using invariant curves. We will discuss how to construct birational maps realizing the Coxeter element in $T(2,q,r)$-diagram using a degree $q$ irreducible curve with a cusp. If time permits we will also discuss how one can generalize this method : (1) realizing the Coxeter element in $T(2,q,r)$ using a reducible curve with a singular point (2) realizing the Coxeter element in $T(p,q,r)$ for $p\ge 3$.