论文标题
随机Kodaira嵌入的预期质量中心
Expected centre of mass of the random Kodaira embedding
论文作者
论文摘要
令$ x \ subset \ mathbb {p}^{n-1} $为平滑的投射品种。对于sl（n，\ mathbb {c}）$中的每个$ g \，它诱导了嵌入$ g \ cdot x \ subset \ subset \ mathbb {p}^{n-1} $由环境线性动作给出的，我们可以将矩阵$ \barμ_x（g）$ g $ g $ g $ g $ g $ g $ g $ g $ g $ g $。关于$ SL（N，\ Mathbb {C}）$的概率度量，由HAAR度量和高斯单位合奏引起的概率，我们证明对质量中心的期望是任何光滑的投影量的身份矩阵的常数倍数。
Let $X \subset \mathbb{P}^{N-1}$ be a smooth projective variety. To each $g \in SL (N , \mathbb{C})$ which induces the embedding $g \cdot X \subset \mathbb{P}^{N-1}$ given by the ambient linear action we can associate a matrix $\barμ_X (g)$ called the centre of mass, which depends nonlinearly on $g$. With respect to the probability measure on $SL (N , \mathbb{C})$ induced by the Haar measure and the Gaussian unitary ensemble, we prove that the expectation of the centre of mass is a constant multiple of the identity matrix for any smooth projective variety.
