Riemann-Roch理论及其应用

Chern-Schwartz-MacPherson类的广义Verdier型Riemann-Roch定理

A generalized Verdier-type Riemann-Roch theorem for Chern-Schwartz-MacPherson classes

本文给出了Chern-Schwartz-MacPherson类的Verdier型Riemann-Roch公式在正则嵌入情形下的亏损的一般公式。这个公式的证明使用了Verdier特化函子的可构造函数版本，以及Chern-Schwartz-MacPherson类的特化性质和相应的光滑态射的Riemann-Roch定理。作为一个非常特殊的情形，我们得到了光滑流形中局部完全交的Milnor-class的一个公式，在超曲面的情形下，它给出了Parusinski-Pragacz的一个结果.

相干层的等变陈特征与Riemann-Roch-Grothendieck定理

Equivariant Chern character for coherent sheaves and Riemann-Roch-Grothendieck

本文在有限群作用的紧致复流形上，为相干层建立等变陈特征理论，并证明相应的Riemann-Roch-Grothendieck定理。

$L^2$-Riemann-Roch for singular complex curves

We present a comprehensive $L^2$-theory for the $\overline\partial$-operator on singular complex curves, including $L^2$-versions of the Riemann-Roch theorem and some applications.

谱不对称性、超对称性与等价黎曼-罗奇缺陷

Spectral asymmetry, supersymmetry and the equivariant Riemann-Roch defect

本文研究了复空间锥状奇点的等价黎曼-罗奇缺陷的两种解释，提出L²旋量空间的新三重划分，并探讨了超对称抵消与黎曼-罗奇缺陷的关系。

An Analytic Grothendieck Riemann Roch Theorem

We extend the Boutet de Monvel Toeplitz index theorem to complex manifold with isolated singularities following the relative $K$-homology theory of Baum, Douglas, and Taylor for manifold with boundary. We apply this index theorem to study the Arveson-Douglas conjecture. Let $\ball^m$ be the unit ball in $\mathbb{C}^m$, and $I$ an ideal in the polynomial algebra $\mathbb{C}[z_1, \cdots, z_m]$. We prove that when the zero variety $Z_I$ is a complete intersection space with only isolated singularities and intersects with the unit sphere $\mathbb{S}^{2m-1}$ transversely, the representations of $\m…