| Abstract: | We prove that every smooth complete intersection (X=X_{d_{1}, ldots , d_{s}}subset mathbb {P}^{sum _{i=1}^{s}d_{i}}) defined by s hypersurfaces of degree (d_{1}, ldots , d_{s}) is birationally superrigid if (5s +1le frac{2(sum _{i=1}^{s}d_{i}+1)}{sqrt{prod _{i=1}^{s}d_{i}}}). In particular, X is non-rational and ({{mathrm{Bir}}}(X)={{mathrm{Aut}}}(X)). We also prove birational superrigidity of singular complete intersections with similar numerical condition. These extend the results proved by Tommaso de Fernex. |
