Related papers: Chow groups of K3 surfaces and spherical objects

We prove that K\"uchle fourfolds $X$ of type d3 have a multiplicative Chow-K\"unneth decomposition. We present some consequences for the Chow ring of $X$.

In this paper, generalizing the techniques of Bour's theorem, we prove that every generic cuspidal edge, more generally, generic $n$-type edge, which is invariant under a helicoidal motion in Euclidean $3$-space admits non-trivial isometric…

We construct an action of the Neron--Severi part of the Looijenga-Lunts-Verbitsky Lie algebra on the Chow ring of the Hilbert scheme of points on a K3 surface. This yields a simplification of Maulik and Negut's proof that the cycle class…

In this paper, we prove a refinement of the Katsura theorem on finite group actions on abelian surfaces such that the quotient is birational to a $K3$ surface. As an application, we compute traces of Frobenius on the Neron--Severi groups of…

This note is a summary of our work [OO] which provides an explicit and global moduli-theoretic framework for the collapsing of Ricci-flat Kahler metrics and we use it to study especially the K3 surfaces case. For instance, it allows us to…

An element in the Brauer group of a general complex projective $K3$ surface $S$ defines a sublattice of the transcendental lattice of $S$. We consider those elements of prime order for which this sublattice is Hodge-isometric to the…

In this paper, we prove a decomposition result for the Chow groups of projectivizations of coherent sheaves of homological dimension $\le 1$. In this process, we establish the decomposition of Chow groups for the cases of Cayley's trick and…

For a smooth quasi-projective scheme $X$ over a field $k$ with an action of a reductive group, we establish a spectral sequence connecting the equivariant and the ordinary higher Chow groups of $X$. For $X$ smooth and projective, we show…

An Ulrich sheaf on an embedded projective variety is a normalized arithmetically Cohen-Macaulay sheaf with the maximum possible number of independent sections. Ulrich sheaves are important in the theory of Chow forms, Boij-Soderberg theory,…

We show that for complex analytic K3 surfaces any torsion class in H^2(X,O_X^*) comes from an Azumaya algebra. In other words, the Brauer group equals the cohomological Brauer group. For algebraic surfaces, such results go back to…

We study the local equivalence problems of curves and surfaces in three dimensional Heisenberg group via Cartans method of moving frames and Lie groups, and find a complete set of invariants for curves and surfaces. For surfaces, in terms…

Let $X$ be a smooth complex cubic fourfold and let $F$ be the variety of lines of $X$. The variety $F$ is known to be a smooth projective hyperkaehler fourfold, which is moreover endowed with a self rational map $\phi : F -\rightarrow F$…

We explain a strategy for distinguishing Brill-Noether loci in the moduli space of curves by studying the lifting of linear systems on curves in polarized K3 surfaces, which motivates a conjecture identifying the maximal Brill-Noether loci…

W. Thurston proved that to a triangulation of the sphere of non-negative combinatorial curvature, one can associate an element in a certain lattice over the Eisenstein integers such that its orbit is a complete invariant of the…

We prove that curves in a non-primitive, base point free, ample linear system on a K3 surface have maximal variation. The result is deduced from general restriction theorems applied to the tangent bundle. We also show how to use…

We compute $CH^*BG_2$ and $CH^*BSpin_7$, using in particular the stratification method introduced by Vezzosi. We also give some information on the Chow rings of the finite groups $G_2(q)$. This new version includes an appendix, which will…

In an earlier paper we generalised the notion of the Tate-Shafarevich group of an elliptic K3 surface to the Tate-Shafarevich group of a polarised K3 surface. In the present note, we complement the result by proving that the…

We study the reduced descendent Gromov-Witten theory of K3 surfaces in primitive curve classes. We present a conjectural closed formula for the stationary theory, which generalizes the Bryan-Leung formula. We also prove a new recursion that…

For an orbifold X and $\alpha \in H^3(X, Z)$, we introduce the twisted cohomology $H^*_c(X, \alpha)$ and prove that the Connes-Chern character establishes an isomorphism between the twisted K-groups $K_\alpha^* (X) \otimes C$ and twisted…

We investigate a strong version of the integral Tate conjecture for 1-cycles on the product of a curve and a surface over a finite field, under the assumption that the surface is geometrically $CH_0$-trivial. By this we mean that over any…