Newton-Puiseux Roots of Jacobian Determinants

具有单个 Puiseux 对的平面曲线奇点的点状 Hilbert 概形的拓扑

Topology of the punctual Hilbert schemes of plane curve singularities with a single Puiseux pair

本文从计算角度重新审视具有单个 Puiseux 对的平面曲线奇点的点状 Hilbert 概形的仿射单元分解定理，并描述了其 Euler 数和 Betti 数。

超椭圆雅可比簇的“指数”挠子群

The "exponential" torsion of superelliptic Jacobians

本文研究超椭圆曲线雅可比簇的$\ell$-幂次挠子群，在温和条件下确定相关$\ell$-进表示的像，证明其行列式像含于有限指数显式$\n\mathbb Z_{\ell}$-格，并验证了一般超椭圆雅可比簇的Hodge、Tate与Mumford-Tate猜想。

收缩除子与二次映射

Contracted divisors and Degree-Two Maps

本文研究了特征零代数闭域上仿射空间的多项式映射，证明了雅可比行列式零点轨迹的每个不可约分支对应于收缩除子或分支除子，并进一步考虑了无收缩除子的二次多项式映射，证明了雅可比行列式不可约、在伽罗瓦对合下反变，且等于唯一分支除子的定义方程。

Pinchuk maps, function fields, and real Jacobian conjectures

Jacobian conjectures (that nonsingular implies invertible) for rational everywhere defined maps of real n-space to itself are considered, with no requirement for a constant Jacobian determinant or a rational inverse. The associated extension of rational function fields must be of odd degree and must have no nontrivial automorphisms. The extensions for the Pinchuk counterexamples to the strong real Jacobian conjecture have no nontrivial automorphisms, but are of degree six. The birational case is proved, the Galois case is clarified but the general case of odd degree remains open. However, cert…

The Abel-Jacobi isomorphism on one cycles on the moduli space of vector bundles with trivial determinant on a curve

We consider the moduli space $\cSU_C^s(r,\cO_C)$ of rank r stable vector bundles with trivial determinant on a smooth projective curve $C$ of genus $g$. We show that the Abel-Jacobi map on the rational Chow group $CH_1(\cSU_C^s(r,\cO_C))_{hom}\otimes \Q$ of one cycles which are homologous to zero, is an isomorphism onto the bottom weight intermediate Jacobian, which is identified with the Jacobian $Jac(C)\otimes \Q$. The result holds whenever $r\geq 2$ and $g\geq 4$.

实Jacobian猜想中的一个尖锐次数界

A sharp degree bound in the real Jacobian conjecture

本文证明了当多项式映射F的p的次数为6时F是单射，并构造了次数为7的非单射例子，从而确定了保证全局单射性的最优次数界为6。