Birationally rigid Fano complete intersections. II

Details Birationally rigid Fano complete intersections. II Birationally rigid Fano complete intersections. II

2011-10-10

arxiv.org/abs/1110.2052v1

Mathematics

Algebraic Geometry

10 pages

Scientific paper

We prove that a generic (in the sense of Zariski topology) Fano complete intersection $V$ of the type $(d_1,...,d_k)$ in ${\mathbb P}^{M+k}$, where $d_1+...+d_k=M+k$, is birationally superrigid if $M\geq 7$, $M\geq k+3$ and $\mathop{\rm max} \{d_i\}\geq 4$. In particular, on the variety $V$ there is exactly one structure of a Mori fibre space (or a rationally connected fibre space), the groups of birational and biregular self-maps coincide, $\mathop{\rm Bir} V= \mathop{\rm Aut} V$, and the variety $V$ is non-rational. This fact covers a considerably larger range of complete intersections than the result of [J. reine angew. Math. {\bf 541} (2001), 55-79], which required the condition $M\geq 2k+1$. The paper is dedicated to the memory of Eckart Viehweg.

Affiliated with

Also associated with

No associations

Rating

Birationally rigid Fano complete intersections. II does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Birationally rigid Fano complete intersections. II, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Birationally rigid Fano complete intersections. II will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-147328