6 papers
Fano threefolds
Yuri Prokhorov
The goal of these lecture notes is to present the modern point of view on the classification of Fano threefolds. We tried to offer a self-consistent treatment of the topics covered…
Birational transformations of threefold -conic bundles
Yuri Prokhorov
A -conic bundle is a contraction of a three-dimensional algebraic variety to a surface~ such that the variety~ has only terminal -fact…
On the birational geometry of -Fano threefolds of large Fano index, II
Yuri Prokhorov
This paper is a sequel to [arXiv:2403.18389]. We investigate the rationality problem for -Fano threefolds of Fano index .
On the birational geometry of sextic threefold hypersurface in
Yuri Prokhorov
We investigate birational properties of hypersurfaces of degree in the weighted projective space . In particular, we prove that any such quasi-smooth hyp…
On the birational geometry of -Fano threefolds of large Fano index, I
Yuri Prokhorov
We investigate the rationality problem for -Fano threefolds of Fano index .
Icosahedron in birational geometry
Yuri Prokhorov
We study quotients of projective and affine spaces by various actions of the icosahedral group. Basically we concentrate on the rationality questions.