Flips and Flops Constructed by GIT Quotient

Brown constructed a series of threefold flips given by the GIT quotient of a hypersurface in ${\mathbb{C}}^5$. In this article, we classify threefold flips and flops which are the GIT quotients of complete intersections in ${\mathbb{C}}^6$. We also show that there are no more new examples as GIT quotients of complete intersections in ${\mathbb{C}}^n$ with $n\ge 7$.