Birational rigidity of complete intersections

Abstract

We prove that every smooth complete intersection X defined by s hypersurfaces of degree d_1, ... , d_s in a projective space of dimension d_1 + ... + d_s is birationally superrigid if 5s +1 is at most 2(d_1 + ... + d_s + 1)/sqrt{d_1...d_s}. In particular, X is non-rational and Bir(X)=Aut(X). We also prove birational superrigidity of singular complete intersections with similar numerical condition. These extend the results proved by Tommaso de Fernex.

To appear in Mathematische Zeitschrift

References in corpus (3)

• Birationally rigid complete intersections of quadrics and cubics
• Birational automorphisms of nodal quartic threefolds
• The volume of a set of arcs on a variety

Cited by in corpus (1)

• The $4n^2$-inequality for complete intersection singularities