Subvarieties of C^n with non-extendible Automorphisms

Actions of groups of birationally extendible automorphisms

We study the actions of a Lie group $G$ by birationally extendible automorphisms on a domain $D\subset C^n$. For a large class of such domains defined by polynomial inequalities, all automorphisms are of this type. In the cases 1) $G$ has finitely many components or 2) the degree of the automorphisms is bounded, we prove that the action of $G$ is projectively linearizable, i.e. there exist a linear representation of $G$ on some $ C^{N+1}$ and a holomorphic $G$-equivariant embedding $i: D\to P^N$, which is a restriction of a rational mapping. As a corollary we obtain as many rational invariant …

The g-periodic subvarieties for an automorphism g of positive entropy on a compact Kahler manifold

For a compact Kahler manifold X and a strongly primitive automorphism g of positive entropy, it is shown that X has at most rank NS(X) of g-periodic prime divisors B_i (i.e., g^s(B_i) = B_i for some s > 0). When X is a projective threefold, every prime divisor containing infinitely many g-periodic curves, is shown to be g-periodic itself (a result in the spirit of the Dynamic Manin-Mumford conjecture).

Classification of toric projective varieties up to projective automorphisms

Toric subvarieties of projective space are classified up to projective automorphisms.

Extensions of isomorphisms of subvarieties in flexile varieties

Let $X$ be a quasi-affine algebraic variety isomorphic to the complement of a closed subvariety of dimension at most $n-3$ in $\C^n$. We find some conditions under which an isomorphism of two closed subvarieties of $X$ can be extended to an automorphism of $X$.

野性自同构猜想的微分类比

A differential analogue of the wild automorphism conjecture

建立了代数动力学中Reichstein-Rogalski-Zhang猜想的微分类比：若射影簇X上存在整体代数向量场v使得(X,v)无真不变子簇，则X为阿贝尔簇；同时研究了阿贝尔簇上具有该性质的向量场。

Tautological rings on Jacobian varieties of curves with automorphisms

Let $J$ be the Jacobian of a smooth projective complex curve $C$ which admits non-trivial automorphisms, and let $A(J)$ be the ring of algebraic cycles on $J$ with rational coefficients modulo algebraic equivalence. We present new tautological rings in $A(J)$ which extend in a natural way the tautological ring studied by Beauville (Compos Math 140(3):683-688, 2004). We then show there exist tautological rings induced on special complementary abelian subvarieties of $J$.