Search arXiv⌕ Search

arXiv subjects

Ivan Cheltsov

Publications and source records attributed to Ivan Cheltsov.

At least 19 recordsLinked to original sources
arXiv2026

Degenerations of elliptic quartics and K-moduli of Fano threefolds

We study the K-moduli space of Fano threefolds obtained by first blowing up $\mathbb{P}^3$ along an elliptic quartic curve $C$ and then blowing up a fiber $\ell_p$ of the exceptional divisor $E \to C$. We prove that this K-moduli space is isomorphic to a VGIT quotient parametrizing pairs $(C,p)$, with linearization induced by the CM line bundle. In particular, we classify all K-(semi/poly)stable members of this deformation family. The main new ingredients in the proof include the geometry of the Hilbert scheme of elliptic quartic curves, deformation theory of Fano--K3 pairs, and optimal bounds on the local volumes of threefold singularities.

math.AG↗
arXiv2026

Unirational del Pezzo surfaces of degree one

We construct explicit unirational del Pezzo surfaces of degree $1$ with arithmetic Picard rank one over $\mathbb{Q}$, $\mathbb{F}_5$, and $\mathbb{C}(t)$. Moreover, we prove that every smooth real geometrically rational surface is unirational over $\mathbb{R}$ if and only if it has a real point.

math.AG↗
arXiv2026

Birational geometry of actions on del Pezzo surfaces

We complete the classification of regular generically free actions of finite groups on del Pezzo surfaces, up to birational equivalence. As a byproduct, we settle several open problems in equivariant birational geometry, e.g., we classify birationally rigid actions on del Pezzo surfaces.

math.AG↗
arXiv2026

G-birationally rigid cubic threefolds

We classify pairs $(X,G)$ consisting of a (possibly singular) cubic threefold $X\subset\mathbb{P}^4$ and a finite subgroup $G\subset\mathrm{Aut}(X)$ such that $X$ is $G$-birationally rigid, i.e., $X$ is a $G$-Mori fiber space (over a point), and $X$ is not $G$-birational to any $G$-Mori fibre space that is not $G$-biregular to $X$.

math.AG↗
arXiv2026

On G-birational rigidity of projective spaces

In this paper, we study finite subgroups $G\subset\mathrm{Aut}(\mathbb{P}^n)$ such that $\mathbb{P}^n$ is $G$-birationally rigid. For each $n\geqslant 3$, we prove that $\mathrm{Aut}(\mathbb{P}^n)$ contains at most finitely many such subgroups up to conjugation. For $n=4,5,7$, we prove that $\mathbb{P}^n$ is $G$-birationally superrigid if $G$ is a primitive subgroup isomorphic to $\mathrm{PSp}_{4}(\mathbf{F}_3)$, $\mathrm{PSU}_4(\mathbf{F}_3)\rtimes\boldsymbol{\mu}_2$, $\mathrm{O}_8^+(\mathbf{F}_2)\rtimes \boldsymbol{\mu}_2$, respectively.

math.AG↗
arXiv2026

A Matsushima theorem for K-polystable polarised smooth Fano threefolds

We prove that if $X$ is a smooth Fano threefold and $L$ is an ample $\mathbb{Q}$-divisor such that $(X,L)$ is K-polystable, then the automorphism group $\operatorname{Aut}(X)$ is reductive. This verifies the reductivity statement predicted by the Yau--Tian--Donaldson conjecture in the setting of smooth Fano threefolds with arbitrary ample polarisation.

math.AG↗
arXiv2025

Simple subgroups of the real space Cremona group

We show that the alternating groups $\mathfrak{A}_5$ and $\mathfrak{A}_6$ are the only finite simple non-abelian subgroups of the group of birational selfmaps of the real three-dimensional projective space.

math.AG↗
arXiv2025

On K-stability of Fano's last Fanos

We study K-stability of smooth Fano threefolds of Picard rank $2$ and degree $22$ which can be obtained by blowing up a smooth complete intersection of two quadrics in $\mathbb{P}^5$ along a conic. We also describe the automorphism groups of these threefolds.

math.AG↗
arXiv2025

Smooth Fano 3-folds satisfying Condition (A)

A smooth variety is said to satisfy Condition (A) if every finite abelian subgroup of its automorphism group has a fixed point. We classify smooth Fano 3-folds that satisfy Condition (A).

math.AG↗
arXiv2025

K-stability of Fano 3-folds in the World of Null-A

A variety is said to satisfy Condition (A) if every finite abelian subgroup of its automorphism group has a fixed point. We show that a smooth Fano 3-fold not satisfying Condition (A) is K-polystable unless it is contained in eight exceptional deformation families (seven of them consists of one smooth member, and one of them has one-parameter moduli).

math.AG↗
arXiv2024

K-moduli of pure states of four qubits

We find all K-polystable limits of divisors in $(\mathbb{P}^1)^4$ of degree $(1,1,1,1)$ and explicitly describe the associated irreducible component of the K-moduli space.

math.AG↗
arXiv2024

Hadamard Langevin dynamics for sampling the l1-prior

Priors with non-smooth log-densities, such as the l1-prior, are widely used in Bayesian inverse problems for their sparsity-inducing properties. Existing Langevin-based sampling methods typically rely on proximal mappings or smooth approximations, which alter the target distribution. We propose an alternative approach based on a Hadamard product parameterization of the l1-norm, leading to a smooth but nonconvex and non-globally Lipschitz potential whose marginal law exactly recovers the desired posterior. The resulting Hadamard Langevin dynamics (HLD) defines a diffusion process that is analytically distinct from proximal or mirror-type Langevin schemes. Our main contribution is a rigorous well-posedness theory for both the continuous and discrete HLD. We establish existence and uniqueness of strong solutions, geometric ergodicity of the continuous dynamics, and convergence of the discretized scheme as the step size tends to zero. These results provide the first theoretical foundation for sampling from nonconvex, nonsmooth posteriors through overparameterized Langevin dynamics.

math.NA↗
arXiv2024

K-stability of pointless del Pezzo surfaces and Fano 3-folds

We explore connections between existence of $\Bbbk$-rational points for Fano varieties defined over $\Bbbk$, a subfield of $\mathbb{C}$, and existence of K\"ahler-Einstein metrics on their geometric models. First, we show that geometric models of del Pezzo surfaces with at worst quotient singularities defined over $\Bbbk\subset\mathbb{C}$ admit (orbifold) K\"ahler--Einstein metrics if they do not have $\Bbbk$-rational points. Then we prove the same result for smooth Fano 3-folds with 8 exceptions. Consequently, we explicitly describe several families of pointless Fano 3-folds whose geometric models admit K\"ahler-Einstein metrics. In particular, we obtain new examples of prime Fano 3-folds of genus $12$ that admit K\"ahler--Einstein metrics. Our result can also be used to prove existence of rational points for certain Fano varieties, for example for any smooth Fano 3-fold over $\Bbbk\subset\mathbb{C}$ whose geometric model is strictly K-semistable.

math.AG↗