arXiv subjects

Dmitrijs Sakovics

Publications and source records attributed to Dmitrijs Sakovics.

5 recordsLinked to original sources

arXiv2019

Projecting Fanos in the mirror

In the paper "Birational geometry via moduli spaces" by I. Cheltsov, L. Katzarkov, and V. Przyjalkowski a new structure connecting toric degenerations of smooth Fano threefolds by projections was introduced; using Mirror Symmetry these connections were transferred to the side of Landau--Ginzburg models. In the paper mentioned above a nice way to connect of Picard rank one Fano threefolds was found. We apply this approach to all smooth Fano threefolds, connecting their degenerations by toric basic links. In particular, we find a lot of Gorenstein toric degenerations of smooth Fano threefolds we need. We implement mutations in the picture as well. It turns out that appropriate chosen toric degenerations of the Fanos are given by toric basic links from a few roots. We interpret the relations we found in terms of Mirror Symmetry.

math.AG↗

arXiv2017

$G$-birational rigidity of the projective plane

Given a surface $S$ and a finite group $G$ of automorphisms of $S$, consider the birational maps $S\dashrightarrow S'$ that commute with the action of $G$. This leads to the notion of a $G$-minimal variety. A natural question arises: for a fixed group $G$, is there a birational $G$-map between two different $G$-minimal surfaces? If no such map exists, the surface is said to be $G$-birationally rigid. This paper determines the $G$-rigidity of the projective plane for every finite subgroup $G\subset\mbox{PGL}_3\left(\mathbb{C}\right)$.

math.AG↗

arXiv2014

Weakly-exceptional quotient singularities in prime dimension

A singularity is said to be weakly-exceptional if it has a unique purely log terminal blow up. This is a natural generalization of the surface singularities of types $D_{n}$, $E_{6}$, $E_{7}$ and $E_{8}$. Since this idea was introduced, quotient singularities of this type have been classified in dimensions up to $5$. This paper looks at such singularities in dimension $p$, where $p$ is an arbitrary prime number.

math.AG↗

arXiv2014

Five-Dimensional Weakly Exceptional Quotient Singularities

A singularity is said to be weakly-exceptional if it has a unique purely log terminal blow up. This is a natural generalization of the surface singularities of types $D_{n}$, $E_{6}$, $E_{7}$ and $E_{8}$. Since this idea was introduced, quotient singularities of this type have been classified in dimensions up to most $4$. This note extends that classification to dimension $5$.

math.AG↗

arXiv2014

Weakly--exceptional quotient singularities

A singularity is said to be weakly--exceptional if it has a unique purely log terminal blow up. In dimension $2$, V. Shokurov proved that weakly--exceptional quotient singularities are exactly those of types $D_{n}$, $E_{6}$, $E_{7}$, $E_{8}$. This paper classifies the weakly--exceptional quotient singularities in dimensions $3$ and $4$.

math.AG↗