29 citations · 102 across the 9 of their papers we have counts for
9 papers
Birational rigidity is not an open property
I. A. Cheltsov, M. M. Grinenko
We construct an example of the birationally rigid complete intersection of a quadric and a cubic in $\PA^5$ with an ordinary double point, which under a small deformation gives a n…
Non-rationality of a three-dimensional Fano variety of index 2 and degree 1
Mikhail Grinenko
We describe the set of Mori structures for a Fano 3-fold of index 2 and degree 1 (the double cone over the Veronese surface). In partiular, it is proved that such a Fano variety is…
Birational models of del Pezzo fibrations
Mikhail Grinenko
This is a preliminary version of the paper for the Lecture Notes Series.
Gorenstein models of del Pezzo surfaces of degree 1 over Dedekind schemes
Mikhail Grinenko
Let R be a Dedekind scheme, its generic point, X and V del Pezzo surfaces of degree 1 over R that are Gorenstein Mori fiber spaces (as 3-folds germs over the ground field). We…
Birational properties of pencils of del Pezzo surfaces of degree 1 and 2
Mikhail Grinenko
We study the birational rigidity problem for smooth Mori fibrations on del Pezzo surfaces of degree 1 and 2. For degree 1 we obtain a complete description of rigid and non-rigid ca…
On a rigidity criterion for del Pezzo fibrations over
Mikhail Grinenko
We discuss the rigidity problem for Mori fibrations on del Pezzo surfaces of degree 1, 2 and 3 over and formulate the following conjecture: such a del Pezzo fibrati…