Birationally rigid complete intersections of high codimension
نویسندگان
چکیده
منابع مشابه
Birationally rigid Fano hypersurfaces
We prove that a smooth Fano hypersurface V = V M ⊂ P M , M ≥ 6, is birationally superrigid. In particular, it cannot be fibered into uniruled varieties by a non-trivial rational map and each birational map onto a minimal Fano variety of the same dimension is a biregular isomorphism. The proof is based on the method of maximal singularities combined with the connectedness principle of Shokurov a...
متن کاملBirationally Rigid Fano Varieties
We give a brief survey of the concept of birational rigidity, from its origins in the two-dimensional birational geometry, to its current state. The main ingredients of the method of maximal singularities are discussed. The principal results of the theory of birational rigidity of higher-dimensional Fano varieties and fibrations are given and certain natural conjectures are formulated.
متن کاملBirationally rigid Fano cyclic covers
then V is a primitive Fano variety of dimensionM , that is, Pic V = ZKV and (−KV ) is ample. The purpose of this note is to sketch a proof of the following Theorem 1. A general (in the sense of Zariski topology) variety V is birationally superrigid. In particular, V admits no non-trivial structures of a rationally connected fibration, any birational map V 99K V ♯ onto a Fano variety with Q-fact...
متن کاملBirationally Rigid Del Pezzo Fibrations
In this paper we study del Pezzo fibrations z : X → P1 of degree 1 and 2 such that X is smooth, rk Pic(X) = 2 and K2 X ∈ NE(X). These are examples of smooth birationally rigid 3-fold Mori fibre spaces. We describe all birational transformations of the 3-fold X into elliptic fibrations, fibrations of surfaces of Kodaira dimension zero, and canonical Fano 3-folds. Let X be a smooth 3-fold1 of Pic...
متن کاملExplicit Examples of Birationally Rigid Fano Varieties
We construct explicit examples of divisorially canonical Fano double spaces. Their direct products are birationally rigid Fano varieties with finitely many structures of a rationally connected fiber space. 2000 Math. Subj. Class. 14E05.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Izvestiya: Mathematics
سال: 2019
ISSN: 1064-5632,1468-4810
DOI: 10.1070/im8782