相关论文: Equivariant unirationality of Fano threefolds

We study cohomological obstructions to equivariant unirationality, with special regard to actions of finite groups on del Pezzo surfaces and Fano threefolds.

We study equivariant unirationality of actions of finite groups on tori of small dimensions.

We study unirationality and rationality of Fano threefolds of degree 18 over nonclosed fields.

We give necessary and sufficient conditions for unirationality and rationality of Fano threefolds of geometric Picard rank-1 over an arbitrary field of zero characteristic.

We study linearizability of actions of finite groups on cubic threefolds with non-isolated singularities.

We study Fano threefolds with~terminal singularities admitting a "minimal" action of a finite group. We prove that under certain additional assumptions such a variety does not contain planes. We also obtain an upper bounds of the number of…

We study linear actions of finite groups in small dimensions, up to equivariant birationality.

We study linearizability of actions of finite groups on cubic threefolds with nonnodal isolated singularities.

We classify the possible images of the action of the group of automorphisms of a smooth Fano threefold on its Picard group. We also study the first group cohomology of the Picard group for families of smooth Fano threefolds.

We give some rationality constructions for Fano threefolds with canonical Gorenstein singularities.

We study degree of irrationality of quasismooth anticanonically embedded weighted Fano 3-fold hypersurfaces that have terminal singularities.

We classify toric Fano threefolds having at worst terminal singularities such that a rank of a $G$-invariant part of a class group equals one, where $G$ is a group acting on the variety by automorphisms.

We study equivariant birationality from the perspective of derived categories. We produce examples of nonlinearizable but stably linearizable actions of finite groups on smooth cubic fourfolds.

We classify smooth Fano threefolds with infinite automorphism groups.

We investigate the rationality problem for $\mathbf{Q}$-Fano threefolds of Fano index $\ge 2$.

We classify some special classes of non-rational Fano threefolds with terminal singularities. In particular, all such hyperelliptic and trigonal varieties are found.

We study the connectedness of the real locus of smooth geometrically rational Fano threefolds and prove a sufficient criterion of $\mathbb{R}$-rationality.

We classify non-factorial nodal Fano threefolds with $1$ node and class group of rank $2$.

We obtain upper bounds on the number of singular points of factorial terminal Fano threefolds.

We shall prove that the threefold studied in the paper "Remarks on an Example of K. Ueno" by F. Campana is unirational. This gives an affirmative answer to a question posed in the paper above and also in the book by K. Ueno, "Classification…