On linearization problems in the plane Cremona group
We study finite non-linearizable subgroups of the plane Cremona group which potentially could be stably linearizable.
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arXiv subjects
Arman Sarikyan
Publications and source records attributed to Arman Sarikyan.
Linearization problem for finite subgroups of the plane Cremona group
We give a complete solution of the linearization problem in the plane Cremona group over an algebraically closed field of characteristic zero.
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Birational rigidity and alpha invariants of Fano varieties
We prove that for every $ε>0$, there is a birationally super-rigid Fano variety $X$ such that $\frac{1}{2}\leqslantα(X)\leqslant \frac{1}{2}+ε$. Also we show that for every $ε>0$, there is a Fano variety $X$ and a finite subgroup $G\subset\mathrm{Aut}(X)$ such that $X$ is $G$-birationally super-rigid, and $α_G(X)<ε$.
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On the Rationality of Fano-Enriques Threefolds
A Fano-Enriques threefold is a three-dimensional non-Gorenstein Fano variety of index 1 with at most canonical singularities. We study the birational geometry of Fano-Enriques threefolds with terminal cyclic quotient singularities. We investigate their rationality, and also provide an example of a Fano-Enriques threefold, whose pliability is 9, i.e. a Fano-Enriques threefold birationally equivalent to exactly 9 Mori fibre spaces in Sarkisov category.
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Equivariant pliability of the projective space
We classify finite subgroups $G\subset\mathrm{PGL}_4(\mathbb{C})$ such that $\mathbb{P}^3$ is not $G$-birational to conic bundles and del Pezzo fibrations, and explicitly describe all $G$-Mori fibre spaces that are $G$-birational to $\mathbb{P}^3$ for these subgroups.
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Toric $G$-Fano Threefolds
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.
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