相关论文: Blown-up boundaries associated with ample cones of…

Bestvina and Mess [BM] proved a remarkable formula for torsion free hyperbolic groups $$ \dim_L\partial\Gamma=cd_L\Gamma-1 $$ connecting the cohomological dimension of a group $\Gamma$ with the cohomological dimension of its boundary…

In this paper we determine all Kobayashi-hyperbolic 2-dimensional complex manifolds for which the group of holomorphic automorphisms has dimension 3. This work concludes a recent series of papers by the author on the classification of…

This paper aims to establish the geometrical finiteness for the natural isometric actions of (birational) automorphism groups on the hyperbolic spaces for K3 surfaces, Enriques surfaces, Coble surfaces, and irreducible symplectic varieties.…

We study degenerating families of hyperbolic dynamics over complex K3 surfaces by means of the theory of hybrid spaces by Boucksom, Favre, and Jonsson. For an analytic family of hyperbolic automorphisms $\{f_t: X_t\to…

We show that a Kleinian surface group, or hyperbolic 3-manifold with a cusp-preserving homotopy-equivalence to a surface, has bounded geometry if and only if there is an upper bound on an associated collection of coefficients that depend…

Any action of a group $\Gamma$ on $\mathbb H^3$ by isometries yields a class in degree three bounded cohomology by pulling back the volume cocycle to $\Gamma$. We prove that the bounded cohomology of finitely generated Kleinian groups…

For an ordinary K3 surface over an algebraically closed field of positive characteristic we show that every automorphism lifts to characteristic zero. Moreover, we show that the Fourier-Mukai partners of an ordinary K3 surface are in…

We consider symmetries of K3 manifolds. Holomorphic symplectic automorphisms of K3 surfaces have been classified, and observed to be subgroups of the Mathieu group $M_{23}$. More recently, automorphisms of K3 sigma models commuting with…

We show that under appropriate assumptions, a blown-up corona of a relatively hyperbolic group is equivariant and the compactification of the universal space for proper action by the blown-up corona is contractible. As a corollary, we…

This is a survey of the Kawamata-Morrison cone conjecture on the structure of Calabi-Yau varieties and more generally Calabi-Yau pairs. We discuss the proof of the cone conjecture for algebraic surfaces, with plenty of examples. We show…

This is a systematic exposition of recent results which completely describe the group of automorphisms and the group of autoequivalences of generic analytic K3 surfaces. These groups, hard to determine in the algebraic case, admit a good…

We construct combinatorial volume forms of hyperbolic three manifolds fibering over the circle. These forms define non-trivial classes in bounded cohomology. After introducing a new seminorm on exact bounded cohomology, we use these…

Using the theory of holes of the Leech lattice and Borcherds method for the computation of the automorphism group of a K3 surface, we give an effective bound for the set of isomorphism classes of projective models of fixed degree for…

We classify the boundaries of hyperbolic groups that have enough quasiconvex codimension-1 surface subgroups with trivial or cyclic intersections.

We show the finiteness of the N\'eron-Severi lattices of complex projective K3 surfaces whose automorphism groups are non-elementary hyperbolic with explicit descriptions, under the assumption that the Picard number $\ge 6$ which is optimal…

We determine the automorphism group of an open log K3 surface with irreducible boundary.

We use our new type of bounded locally homeomorphic quasiregular mappings in the unit 3-ball to address long standing problems for such mappings. The construction of such mappings comes from our construction of non-trivial compact…

A hypergeometric group is a matrix group modeled on the monodromy group of a generalized hypergeometric differential equation. This article presents a fruitful interaction between the theory of hypergeometric groups and dynamics on K3…

We prove the convex combination theorem for hyperbolic n-manifolds. Applications are given both in high dimensions and in 3 dimensions. One consequence is that given two geometrically finite subgroups of a discrete group of isometries of…

For $\mathbb Z_3$-orbifold limits of K3, we provide a counterpart to the extensive studies by Nikulin and others of the geometry and symmetries of classical Kummer surfaces. In particular, we determine the group of holomorphic symplectic…