76 citations · 395 across the 39 of their papers we have counts for
47 papers
Factoriality and birational rigidity of two families of singular quartic three-folds
Aleksandr V. Pukhlikov
In this paper we study two families of three-dimensional quartics in the complex projective space : hypersurfaces with a unique quadratic singularity of rank 3, whic…
Birational rigidity of quartic three-folds with a double point of rank 3
Aleksandr V. Pukhlikov
We prove that a general three-dimensional quartic in the complex projective space , the only singularity of which is a double point of rank 3, is a birationally…
Affine complements in the projective space with the trivial group of automorphisms
Aleksandr V. Pukhlikov
We construct a new class of affine complements with the trivial group of automorphisms, where is a rational hypersurface, is…
Birationally rigid hypersurfaces with quadratic singularities of low rank
Aleksandr V. Pukhlikov
It is shown that hypersurfaces of degree in , , with at most quadratic singularities of rank at least 3, satisfying certain conditions of general p…
Rationally connected Galois covers of Fano-Mori fibre spaces
Aleksandr V. Pukhlikov
For Fano-Mori fibre spaces , every fibre of which is a primitive Fano variety with the global canonical threshold at least 1, and which are stable with respect to b…
Birationally rigid Fano-Mori fibre spaces
Aleksandr V. Pukhlikov
In this paper we prove the birational rigidity of Fano-Mori fibre spaces , every fibre of which is a Fano complete intersection of index 1 and codimension $k\geqsla…