Birational Mori fiber structures of Q -Fano 3-fold weighted complete intersections, III

Abstract

This is a continuation of a series of articles studying the birational Mori fiber structures of anticanonically embedded $\mathbb{Q}$-Fano $3$-fold weighted complete intersections of codimension $2$. We have proved that $19$ families consist of birationally rigid varieties and $14$ families consist of birationally birigid varieties. Our aim here is to continue the work systematically and prove that, among the remaining $52$ families, $21$ families consist of birationally birigid varieties.