Related papers: Algebraic cycles on some special hyperk\"ahler var…

We prove that for any polarized symplectic automorphism of the Fano variety of lines of a cubic fourfold (equipped with the Pl\"ucker polarization), the induced action on the Chow group of 0-cycles is identity, as predicted by…

Let X be a smooth variety over a field k, and l be a prime number invertible in k. We study the (\'etale) unramified H^3 of X with coefficients Q_l/Z_l(2) in the style of Colliot-Th\'el\`ene and Voisin. If k is separably closed, finite or…

We will show that the singular cohomology groups of a smooth quasi-projective complex variety relative to a normal crossing divisor can be described in terms of delta-admissible chains. Roughly speaking, a delta-admissible chain is a…

Let $X$ be a smooth projective variety over an arbitrary field $k$ of characteristic zero. We explore infinitesimal deformations of the Chow group $CH^{p}(X)$ via its formal completion $\widehat{CH}^{p}$, a functor defined on the category…

For any algebraic scheme $X$ and every $(n,\mathscr{L})\in \mathbb{Z}\times \text{Pic}(X)$ we define an associated involution of its Chow group $A_*X$, and show that certain characteristic classes of (possibly singular) hypersurfaces in a…

Let $G$ be an arbitrary finite group and fix a prime number $p$. The McKay conjecture asserts that $G$ and the normalizer in $G$ of a Sylow $p$-subgroup have equal numbers of irreducible characters with degrees not divisible by $p$. The…

We give a construction of algebraic differential characters, receiving classes of algebraic bundles with connection, lifitng the Chern-Simons invariants defined with S. Bloch, the classes in the Chow group and the analytic secondary…

Consider an external product of a higher cycle and a usual cycle which is algebraically equivalent to zero. Assume there exists an algebraically closed subfield k such that the higher cycle and its ambient variety are defined over k, but…

We study families of rational curves on certain irreducible holomorphic symplectic varieties. In particular, we prove that any ample linear system on a projective holomorphic symplectic variety of K3[n]-type contains a uniruled divisor. As…

A smooth intersection $Y$ of two quadrics in $\mathbb{P}^{2g+1}$ has Hodge level 1. We show that such varieties $Y$ have a multiplicative Chow-K\"unneth decomposition, in the sense of Shen-Vial. As a consequence, a certain tautological…

We show that the pseudoeffective cone of $k$-cycles on a complete complexity one $T$-variety is rational polyhedral for any $k$, generated by classes of $T$-invariant subvarieties. When $X$ is also rational, we give a presentation of the…

We prove that the space of coinvariants of functions on an affine variety by a Lie algebra of vector fields whose flow generates finitely many leaves is finite-dimensional. Cases of the theorem include Poisson (or more generally Jacobi)…

The semi-simplicity of the Hodge group is proved for a simple Abelian variety with a stable reduction of odd toric (reductive) rank. If, besides, the dimension of the Abelian variety is an odd integer, then the Hodge conjecture on algebraic…

Suppose $\mathfrak{g}=\mathfrak{g}_{\bar 0}+\mathfrak{g}_{\bar 1} is a Lie superalgebra of queer type or periplectic type over an algebraically closed field $\textbf{k}$ of characteristic $p>2$. In this article, we initiate preliminarily to…

We prove that the rational Chow motive of a six dimensional hyper-K\"{a}hler variety obtained as symplectic resolution of O'Grady type of a singular moduli space of semistable sheaves on an abelian surface $A$ belongs to the tensor category…

We develop the theory of quasi--invariant (resp. strongly quasi--invariant) states under the action of a group $G$ of normal $*$--automorphisms of a $*$--algebra (or von Neumann alegbra) $\mathcal{A}$. We prove that these states are…

We investigate Beauville's conjecture on the Chow ring of irreducible symplectic varieties. For special irreducible symplectic varieties we relate it to a conjecture on the existence of rational Lagrangian fibrations, which proves…

Let K be a CM-field, i.e., a totally complex quadratic extension of a totally real field F. Let X be a g-dimensional abelian variety admitting an algebra embedding of F into the rational endomorphisms of X. Let A be the product of X and…

Making use of the recent theory of noncommutative motives, we prove that every additive invariant satisfies Galois descent. Examples include mixed complexes, Hochschild homology, cyclic homology, periodic cyclic homology, negative cyclic…

Let $Y$ be a compact Gorenstein analytic space with only isolated singularities and trivial dualizing sheaf. A recent paper of Imagi studies the deformation theory of $Y$ in case the singularities of $Y$ are weighted homogeneous and…