K. Loginov

activity

20142026

most citedHilbert-Samuel sequences of homogeneous finite type

6 citations · 15 across the 20 of their papers we have counts for

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24 papers · 1 filter

math.AG2026

Three-dimensional noncommutative Fano minifolds

Konstantin Loginov, Dmitri Orlov

We give a construction of the previously announced family of three-dimensional noncommutative Fano minifolds of Euler degree $72$ . We prove that their defining $Z$ -algebra…

math.AG2026

Non-commutative Fano varieties and three-dimensional minifolds

Konstantin Loginov, Dmitri Orlov

We introduce notions of non-commutative Fano varieties and non-commutative minifolds, and study the latter in dimension three. We prove that the Euler matrices of full exceptional…

math.AG2026

Unirational del Pezzo surfaces of degree one

Ivan Cheltsov, Konstantin Loginov, Dmitri Orlov +1

We construct explicit unirational del Pezzo surfaces of degree $1$ with arithmetic Picard rank one over $Q$ , $F_{5}$ , and $C (t)$ . Moreover, we prove that e…

math.AG2026

Actions of $(Z /4)^{4}$ on rationally connected threefolds

Konstantin Loginov

Let $G = (Z /4)^{4}$ . We prove that if $X$ is a rationally connected threefold with a faithful action of $G$ , then $X$ is $G$ -birational to the Fermat quartic threefold. If $X$ …

math.AG2026

Dual complexes of qdlt Fano type models and strong complete regularity

Jihao Liu, Konstantin Loginov

We introduce birational strong complete regularity and strong complete regularity, two numerical invariants for pairs of (relative) Fano type. They are defined using variants of qd…

math.AG2026

On the coregularity of del Pezzo surfaces with du Val singularities

Konstantin Loginov, Andrey Trepalin

We compute the coregularity of del Pezzo surfaces with du Val singularities. To this aim, we study the relation between del Pezzo surfaces of degree $1$ and elliptic fibrations. It…

math.AG2025

Finite abelian groups acting on rationally connected threefolds II: groups of K3 type

Konstantin Loginov, Antoine Pinardin, Zhijia Zhang

We study finite abelian groups acting on three-dimensional rationally connected varieties. We concentrate on the groups of K3 type, that is, abelian extensions by a cyclic group of…

math.AG2025

Finiteness of projective pluricanonical representation for automorphisms of complex manifolds

Konstantin Loginov, Constantin Shramov

We study the action of the group of bimeromorphic automorphisms $Bim (X)$ of a compact complex manifold $X$ on the image of the pluricanonical map, which we call the projec…

math.AG2025

G-coregularity of del Pezzo surfaces

Konstantin Loginov, Victor Przyjalkowski, Andrey Trepalin

We introduce and study the notion of $G$ -coregularity of algebraic varieties endowed with an action of a finite group $G$ . We compute $G$ -coregularity of smooth del Pezzo surfaces…

math.AG2024★ 1 cited

Birational invariants of volume preserving maps

Konstantin Loginov, Zhijia Zhang

We study the group of birational automorphisms of the $n$ -dimensional projective space that preserve the standard torus invariant volume form with logarithmic poles. We prove that…

math.AG2024★ 1 cited

Finite abelian groups acting on rationally connected threefolds I: Groups of product type

Konstantin Loginov

We initiate the study of finite abelian groups that faithfully act on $3$ -dimensional rationally connected varieties. We show that these groups can be naturally divided into three…

math.AG2024★ 1 cited

Toric models of smooth Fano threefolds

Konstantin Loginov, Joaquín Moraga, Artem Vasilkov

We prove that a general rational smooth Fano threefold admits a toric model. More precisely, for a general rational smooth Fano threefold $X$ , we show the existence of a boundary d…

math.AG2024

K-stability of Fano threefolds of rank 3 and degree 14

Grigory Belousov, Konstantin Loginov

We prove that all general smooth Fano threefolds of Picard rank $3$ and degree $14$ are K-stable, where the generality condition is stated explicitly.

math.AG2023

Coregularity of smooth Fano threefolds

Artem Avilov, Konstantin Loginov, Victor Przyjalkowski

We study the coregularity of smooth Fano threefolds. We prove that for 100 out of 105 families of smooth Fano threefolds, a general member in the family has coregularity 0; moreove…

math.AG2023

Boundedness of log Fano pairs with certain K-stability

Konstantin Loginov, Chuyu Zhou

We prove several boundedness results for log Fano pairs with certain K-stability. In particular, we prove that K-semistable log Fano pairs of Maeda type form a log bounded family.…

math.AG2022★ 1 cited

Jordan property for groups of bimeromorphic self-maps of complex manifolds with large Kodaira dimension

Konstantin Loginov

We prove that the image of the pluricanonical representation of a group of bimeromorphic automorphisms of a complex manifold has bounded finite subgroups. As a consequence, we show…

math.AG2022

K-stability of Fano threefolds of rank 4 and degree 24

Grigory Belousov, Konstantin Loginov

We prove that all smooth Fano threefolds of rank 4 and degree 24 are K-stable.

math.AG2021

K-polystability of 3-dimensional log Fano pairs of Maeda type

Konstantin Loginov

Using the Abban-Zhuang theory and the classification of three-dimensional log smooth log Fano pairs due to Maeda, we prove that threefold log Fano pairs $(X, D)$ of Maeda type with…

math.AG2021

A note on 3-subgroups in the space Cremona group

Konstantin Loginov

We prove that a finite $3$ -group in the Cremona group $Cr_{3} (C)$ can be generated by at most $4$ elements. This provides the last missing piece in bounding the ran…

math.AG2020

Maximal log Fano manifolds are generalized Bott towers

Konstantin Loginov, Joaquín Moraga

We prove that maximal log Fano manifolds are generalized Bott towers. As an application, we prove that in each dimension, there is a unique maximal snc Fano variety satisfying Frie…

math.AG2020

Bounding non-rationality of divisors on 3-fold Fano fibrations

Caucher Birkar, Konstantin Loginov

In this paper we investigate non-rationality of divisors on 3-fold log Fano fibrations $(X, B) \to Z$ under mild conditions. We show that if $D$ is a component of $B$ with coefficien…

math.AG2019

On semistable degenerations of Fano varieties

Konstantin Loginov

Consider a family of Fano varieties $π : X ⟶ B ∋ o$ over a curve germ with a smooth total space $X$ . Assume that the generic fiber is smooth and the special fiber $F=…

math.AG2018

On non-rational fibers of del Pezzo fibrations over curves

Konstantin Loginov

We consider threefold del Pezzo fibrations over a curve germ whose central fiber is non-rational. Under the additional assumption that the singularities of the total space are at w…

math.AG2017★ 5 cited

Standard models of degree $1$ del Pezzo fibrations

Konstantin Loginov

We construct a standard birational model (a model that has Gorenstein canonical singularities) for the three-dimensional del Pezzo fibrations $π : X ⟶ C$ of d…

Three-dimensional noncommutative Fano minifolds

Non-commutative Fano varieties and three-dimensional minifolds

Unirational del Pezzo surfaces of degree one

Actions of (Z/4)4 on rationally connected threefolds

Dual complexes of qdlt Fano type models and strong complete regularity

On the coregularity of del Pezzo surfaces with du Val singularities

Finite abelian groups acting on rationally connected threefolds II: groups of K3 type

Finiteness of projective pluricanonical representation for automorphisms of complex manifolds

G-coregularity of del Pezzo surfaces

Birational invariants of volume preserving maps

Finite abelian groups acting on rationally connected threefolds I: Groups of product type

Toric models of smooth Fano threefolds

K-stability of Fano threefolds of rank 3 and degree 14

Coregularity of smooth Fano threefolds

Boundedness of log Fano pairs with certain K-stability

Jordan property for groups of bimeromorphic self-maps of complex manifolds with large Kodaira dimension

K-stability of Fano threefolds of rank 4 and degree 24

K-polystability of 3-dimensional log Fano pairs of Maeda type

A note on 3-subgroups in the space Cremona group

Maximal log Fano manifolds are generalized Bott towers

Bounding non-rationality of divisors on 3-fold Fano fibrations

On semistable degenerations of Fano varieties

On non-rational fibers of del Pezzo fibrations over curves

Standard models of degree 1 del Pezzo fibrations

Actions of $(Z /4)^{4}$ on rationally connected threefolds

Standard models of degree $1$ del Pezzo fibrations