Birational Mori fiber structures of $\mathbb{Q}$-Fano $3$-fold weighted complete intersections, III

Abstract

This is a continuation of a series of papers 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 consists of birationally rigid varieties and $14$ families consists of birationally birigid varieties. The aim of this paper is to continue the work systematically and prove that, among the remaining $52$ families, $21$ families consist of birationally birigid varieties.

53 pages

References in corpus (4)

• Birationally rigid Fano threefold hypersurfaces
• Birational Mori fiber structures of Q-Fano 3-fold weighted complete intersections, II
• Non-rigid quartic 3-folds
• $\mathbb{Q}$-Fano threefolds with three birational Mori fiber structures

Cited by in corpus (4)

• Birationally rigid complete intersections of high codimension
• Birationally rigid complete intersections of codimension two
• $2n^2$-inequality for $c{A}_1$ points and applications to birational rigidity
• $\mathbb{Q}$-Fano threefolds with three birational Mori fiber structures