Fiber products under toric flops and flips

Tsung-Chen Chen, Hui-Wen Lin, Sz-Sheng Wang

Let $\Sigma$ and ${\Sigma }^{\prime }$ be two refinements of a fan ${\Sigma }_0$ and $f:X_{\Sigma }⇢X_{{\Sigma }^{\prime }}$ be the birational map induced by $X_{\Sigma }\to X_{{\Sigma }_0}\leftarrow X_{{\Sigma }^{\prime }}$. We show t…