arXiv subjects

Anastasia V. Vikulova

Publications and source records attributed to Anastasia V. Vikulova.

9 recordsLinked to original sources

arXiv2026

Birational automorphism groups of Severi-Brauer surfaces over the field of rational numbers

We prove that the only non-trivial finite subgroups of birational automorphism group of non-trivial Severi--Brauer surfaces over the field of rational numbers are $\mathbb{Z}/3\mathbb{Z}$ and $(\mathbb{Z}/3\mathbb{Z})^2.$ Moreover, we show that $(\mathbb{Z}/3\mathbb{Z})^2$ is contained in $\mathrm{Bir}(V)$ for any Severi--Brauer surface $V$ over a field of characteristic different from $2$ and $3$, and $(\mathbb{Z}/3\mathbb{Z})^3$ is contained in $\mathrm{Bir}(V)$ for any Severi--Brauer surface $V$ over a field of characteristic different from $2$ and $3$ which contains a non-trivial cube root of unity.

math.AG↗

arXiv2026

The largest automorphism group of del Pezzo surface of degree $2$ without points

We construct an example of a field and a smooth del Pezzo surface of degree $2$ over this field without points such that its automorphism group is isomorphic to $\mathrm{PSL}_2(\mathbb{F}_7) \times \mathbb{Z}/2\mathbb{Z},$ which is the largest possible automorphism group of del Pezzo surfaces of degree $2$ over an algebraically closed field of characteristic zero.

math.AG↗

arXiv2026

Smooth $l$-Fano weighted complete intersections

In this paper we prove that for $n$-dimensional smooth $l$-Fano well-formed weighted complete intersections that are not isomorphic to a usual projective space, the upper bound for $l$ is equal to $\lceil \log_2(n+2) \rceil-1.$ We also prove that the only $l$-Fano variety of dimension $n$ among such manifolds, where $ \lceil \log_3(n+2) \rceil \leqslant l \leqslant \lceil \log_2(n+2) \rceil -1$, is a complete intersection of quadrics in a usual projective space.

math.AG↗

arXiv2026

Composition of Sarkisov links between del Pezzo surfaces

We prove that for any two birationally equivalent del Pezzo surfaces of Picard rank one over a perfect field there is a birational map between them such that it is decomposed in a composition of at most two Sarkisov links.

math.AG↗

arXiv2025

The most symmetric smooth cubic surface

In this paper for any field of characteristic different from 2 we find the largest automorphism group of a smooth cubic surface over this field. Moreover, we prove that for a given field a smooth cubic surface with the largest automorphism group is unique up to isomorphism.

math.AG↗

arXiv2024

An elementary description of nef cone for irreducible holomorphic symplectic manifolds

We describe MBM classes for irreducible holomorphic symplectic manifolds of K3 and Kummer types. These classes are the monodromy images of extremal rational curves which give the faces of the nef cone of some birational model. We study the connection between our results and A. Bayer and E. Macr\`ı's theory. We apply the numerical method of description due to E. Amerik and M. Verbitsky in low dimensions to the K3 type and Kummer type cases.

math.AG↗

arXiv2024

The most symmetric smooth cubic surface over a finite field of characteristic $2$

In this paper we find the largest automorphism group of a smooth cubic surface over any finite field of characteristic $2.$ We prove that if the order of the field is a power of $4,$ then the automorphism group of maximal order of~a~smooth cubic surface over this field is $\mathrm{PSU}_4(\mathbb{F}_2).$ If the order of the field of characteristic $2$ is not a power of $4,$ then we prove that the automorphism group of maximal order of a smooth cubic surface over this field is the symmetric group of degree $6.$ Moreover, we prove that smooth cubic surfaces with such properties are unique up to isomorphism.

math.AG↗

arXiv2022

Jordan constant for Cremona group of rank 2 over a finite field

In this paper we find the exact value of the Jordan constant for Cremona group of rank $2$ over all finite fields. During the proof we construct a cubic surface over $\mathbb{F}_2$ with a regular action of the group $\mathrm{S}_6$ which is the maximal automorphism group of cubic surfaces over $\mathbb{F}_2.$ Moreover, we prove the uniqueness up to isomorphism of such a cubic surface.

math.AG↗

arXiv2019

Parallel coordinates in three dimensions and sharp spectral isoperimetric inequalities

In this paper we show how the method of parallel coordinates can be extended to three dimensions. As an application, we prove the conjecture of Antunes, Freitas and Krejčiřík \cite{AFK} that "the ball maximises the first Robin eigenvalue with negative boundary parameter among all convex domains of equal surface area" under the weaker restriction that the boundary of the domain is diffeomorphic to the sphere and convex or axiconvex. We also provide partial results in arbitrary dimensions.

math.SP↗