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Alexandra Kuznetsova

Publications and source records attributed to Alexandra Kuznetsova.

11 recordsLinked to original sources
arXiv2026

Projective subvarieties of Bogomolov-Guan manifolds and quasi-diagonals in products of elliptic curves

We study complex subvarieties in certain non-Kahler holomorphically symplectic manifolds $X$, called the Bogomolov-Guan manifolds. Let $E$ be an elliptic curve, $L$ an ample line bundle on $E$, $S\subset E^2$ a complex curve, and $p_1, p_2$ the corresponding projections of $S$ to $E$. The curve $S$ is called a quasi-diagonal if $p_1^*L\otimes p_2^* L^{-1}$ is a torsion line bundle. We show that there are at most countably many quasi-diagonals for any $(E,L)$. Using the quasi-diagonals, we classify the projective subvarieties in the Bogomolov-Guan manifold. The Bogomolov-Guan manifold is equipped with a Lagrangian fibration $\pi:\; X \to {\Bbb C} P^n$. We show that an irreducible complex subvariety $Z\subset X$ is Moishezon if and only if $\pi(Z)$ is a point or a certain complex curve which is described in terms of quasi-diagonals. This is used to prove that for a general Bogomolov-Guan manifold, any projective subvariety belongs to a fiber of $\pi$.

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arXiv2025

Automorphisms of bounded growth

We study birational automorphisms of algebraic varieties of bounded growth, i.e. such that the norms of the inverse images ${(f^n)}^* \colon \mathrm{NS}(X)\to \mathrm{NS}(X)$ of the powers of the automorphism $f\in\mathrm{Bir}(X)$ are bounded above for $n\geqslant 0$. We prove that some power of an infinite order automorphism of a variety $X$ with such property factors either through an infinite order translation on the Albanese variety of $X$ or through an infinite order regular automorphism of $\mathbb{P}^m$ for $m\geqslant 1$. We deduce from this that if a rationally connected threefold admits an infinite order automorphism whose growth is bounded then the threefold is rational and an iterate of the automorphism is birationally conjugate to a regular automorphism of $\mathbb{P}^3$, a generalization of Blanc and Deserti's result.

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arXiv2023

Families of automorphisms of abelian varieties

We consider some algebraic aspects of the dynamics of an automorphism on a family of polarized abelian varieties parameterized by the complex unit disk. When the action on the cohomology of the generic fiber has no cyclotomic factor, we prove that such a map can be made regular only if the family of abelian varieties does not degenerate. As a contrast, we show that families of translations are always regularizable. We further describe the closure of the orbits of such maps, inspired by results of Cantat and Amerik-Verbitsky.

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arXiv2023

Double covers of smooth quadric threefolds with Artin-Mumford obstructions to rationality

We study obstructions to rationality on a nodal Fano threefold $M$ that is a double cover of a smooth quadric threefold ramified over an intersection with a quartic threefold in $\mathbb{P}^4$. We prove that if $M$ admits an Artin--Mumford obstruction to rationality then it lies in one of three explicitly described families. Conversely, a general element of any of these families admits an Artin--Mumford obstruction to rationality. Only one of these three families was known before; other two families of nodal Fano threefolds with obstructions to rationality are new.

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arXiv2022

Regularizations of positive entropy pseudo-automorphisms

We study positive entropy birational automorphisms of threefolds. We identify some conditions which imply that such an automorphism is non-regularizable. We show that this criterion applies in the example of a positive entropy birational automorphism of $\mathbb{P}^3$ constructed by J. Blanc, thus showing that for a general choice of parameters it is non-regularizable. Additionally, we establish a criterion which proves that the automorphism in this example does not preserve a structure of a fibration over a surface.

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arXiv2022

ConsumerCheck: A Software for Analysis of Sensory and Consumer Data

ConsumerCheck is an open source data analysis software tailored for analysis of sensory and consumer data. Since some of the implemented methods are generic, such as PCA, PLSR and PCR, other data from other domains may also be analysed with ConsumerCheck. The software comes with a graphical user interface and as such provides non-statisticians and users without programming skills free access to a number of widely used analysis methods within the field of sensory and consumer science. Computational results are presented in plots that are easily generated from the tree-controls within the graphical user interfaces. Since the construction of conjoint analysis models is not always straightforward, ConsumerCheck provides three previously defined model structures of different complexity. ConsumerCheck is an ongoing research project and the objective is to implement further statistical methods over time.

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arXiv2021

Geometry and automorphisms of non-Kähler holomorphic symplectic manifolds

We consider the only one known class of non-Kähler irreducible holomorphic symplectic manifolds, described in the works of D. Guan and the first author. Any such manifold $Q$ of dimension $2n-2$ is obtained as a finite degree $n^2$ cover of some non-Kähler manifold $W_F$ which we call the base of $Q$. We show that the algebraic reduction of $Q$ and its base is the projective space of dimension $n-1$. Besides, we give a partial classification of submanifolds in $Q$, describe the degeneracy locus of its algebraic reduction, and prove that the automorphism group of $Q$ satisfies the Jordan property.

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arXiv2020

Finite 3-subgroups in Cremona group of rank 3

We consider 3-subgroups in groups of birational automorphisms of rationally connected threefolds and show that any 3-subgroup can be generated by at most five elements. Moreover, we study groups of regular automorphisms of terminal Fano threefolds and prove that in all cases which are not among several explicitly described exceptions any 3-subgroup of such group can be generated by at most four elements.

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arXiv2019

Sextic double solids with Artin-Mumford obstructions to rationality

We study a double solid X branched along a nodal sextic surface in a projective space and the 2-torsion subgroup in the third integer cohomology group of a resolution of singularities of X. This group can be considered as an obstruction to rationality of X. Studying this group we conclude that all sextic double solids admitting non-trivial obstructions to rationality are branched along determinantal surfaces of very specific type and we provide an explicit list of them.

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arXiv2016

Endomorphisms of projective bundles over a certain class of varieties

Let $B$ be a simply-connected projective variety such that the first cohomology groups of all line bundles on $B$ are zero. Let $E$ be a vector bundle over $B$ and $X={\mathbb P} (E)$. It is easily seen that a power of any endomorphism of $X$ takes fibers to fibers. We prove that if $X$ admits an endomorphism which is of degree greater than one on the fibers then $E$ splits into a direct sum of line bundles.

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