Birational boundedness of rationally connected log Calabi-Yau pairs with fixed index

Abstract

We show that the set of rationally connected projective varieties $X$ of a fixed dimension such that $(X,B)$ is klt, and $-l(K_X+B)$ is Cartier and nef for some fixed positive integer $l$, is bounded modulo flops.

12 pages, comments are very welcome; final version, to appear in Algebr. Geom. Phys