Birationally rigid complete intersections of quadrics and cubics

TL;DR

This paper establishes the birational superrigidity of generic Fano complete intersections of quadrics and cubics under specific dimensional and type conditions, advancing the understanding of their birational properties.

Contribution

It proves birational superrigidity for a broad class of Fano complete intersections of quadrics and cubics, including new cases in dimensions 10 and 11.

Findings

Proves birational superrigidity for generic Fano complete intersections of specified types.

Extends known results to higher dimensions and new families of Fano varieties.

Includes minor corrections and clarifications in the latest version.

Abstract

We prove birational superrigidity of generic Fano complete intersections $V$ of type $2^{k_1}\cdot 3^{k_2}$ in the projective space ${\mathbb P}^{2k_1+3k_2}$, under the condition that $k_2\geq 2$ and $k_1+2k_2=\mathop{\rm dim} V\geq 12$, and of a few families of Fano complete intersections of dimension 10 and 11. This is the third version: minor corrections were made, including a few typos.