9 citations · 13 across the 3 of their papers we have counts for
6 papers · 1 filter
On the -inequality
Aleksandr Pukhlikov
We give a complete proof of the so called -inequality, a local inequality for the self-intersection of a movable linear system at an isolated centre of a non canonical singul…
Birational geometry of singular Fano varieties
Aleksandr Pukhlikov
We prove divisorial canonicity of Fano hypersurfaces and double spaces of general position with elementary singularities.
Birationally rigid Fano cyclic covers
Aleksandr V. Pukhlikov
We prove birational superrigidity of Fano cyclic covers of index 1 over hypersurfaces in the projective space.
Birationally rigid varieties with a pencil of Fano double covers. I
Aleksandr V. Pukhlikov
We prove that a general Fano fibration , the fiber of which is a double Fano hypersurface of index 1, is birationally superrigid provided it is sufficie…
Birationally rigid Fano varieties
Aleksandr V. Pukhlikov
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…
Essentials of the method of maximal singularities
Aleksandr V. Pukhlikov
A consistent exposition of the arguments and constructions of the method of maximal singularities, the aim of which is to describe birational iso/automorphisms of Fano varieties an…