The dual complex of log Calabi-Yau pairs on Mori fibre spaces

Abstract

In this paper we show that the dual complex of a dlt log Calabi-Yau pair $(Y,\Delta )$ on a Mori fibre space $\pi :Y\to Z$ is a finite quotient of a sphere, provided that either the Picard number of $Y$ or the dimension of $Z$ is $\le 2$. This is a partial answer to Question 4 in "The dual complex of Calabi-Yau pairs" by Kollár and Xu.

24 pages; published in Advances in Mathematics 364 (2020), 107009