A note on the Poincar'e series of the invariants of ternary forms

MacMahon Partition Analysis and the Poincaré series of the algebras of invariants of ternary, quaternary and quinary forms

By using MacMahon partition analysis technique, the Poincaré series for the algebras of invariants of the ternary, quaternary and quinary forms of small orders are calculated.

Chiral Poincaré duality

The aim of this note is to prove the analogue of Poincaré duality in the chiral Hodge cohomology.

关于三元四次型的希尔伯特定理的一个初等证明：一些补充

An elementary proof of Hilbert's theorem on ternary quartics: Some complements

本文在2012年提出的初等证明基础上，进一步简化了Hilbert关于实系数非负三元四次型可表示为三个二次型平方和的定理证明。

椭圆 Schubert 类与庞加莱对偶

Elliptic Schubert Classes and the Poincare Duality

本文通过 Kostant-Kumar 方法，证明了 Schubert 簇的椭圆类满足庞加莱对偶性。

复 Bott-Chern 上同调中的广义 Lelong–Poincaré 公式

Generalised Lelong-Poincaré formula in complex Bott-Chern cohomology

本文用拓扑方法证明广义 Lelong–Poincaré 公式，表明在零点轨迹纯余维等于全纯向量丛秩时，最高陈类等于其概形零点轨迹在复 Bott-Chern 上同调中的闭链类。

Configuration spaces of $\mathbb{C} \setminus k$

In this note, we collect mostly known formulas and methods to compute the standard and virtual Poincaré polynomials of the configuration spaces of the plane $\mathbb{C} \setminus k$ with $k$ deleted points and compare the answers.