Ivan Beldiev

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20222025

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math.AG2025

The Lie algebra of polynomial vector fields on the affine space is $2$ -generated

Ivan Beldiev

We prove that the infinite-dimensional Lie algebra of polynomial vector fields on the affine space $\KK^n$ is generated by two explicitly given elements.

math.AG2024

On Picard Number and Dimension of Algebraic Homogeneous Spaces

Ivan Beldiev, Dmitry Timashev

An algebraic variety $X$ is called a homogeneous space if there exists a transitive regular action of an algebraic group on $X$ . We prove inequalities between the dimension of a ho…

math.AG2022

The Group of Isometries of $K_{0} (P_{n})$

Ivan Beldiev

We study the group of isometries of the Grothendieck group $K_{0} (P_{n})$ equipped with the standard Euler form $χ$ defined by $χ (E, F) = \sum_{ν} (- 1)^{ν} dim E x t^{ν} (E, F)$ . We prov…

The Lie algebra of polynomial vector fields on the affine space is 2-generated

On Picard Number and Dimension of Algebraic Homogeneous Spaces

The Group of Isometries of K0​(Pn​)

The Lie algebra of polynomial vector fields on the affine space is $2$ -generated

The Group of Isometries of $K_{0} (P_{n})$