论文标题
Abel-Jacobi地图和拉回度量的曲率
Abel-Jacobi map and curvature of the pulled back metric
论文作者
论文摘要
令$ x $为紧凑的连接的riemann属，至少两个。 Abel-Jacobi Map $φ：{\ rm sym}^d（x）\ rightarrow {\ rm pic}^d（x）$是嵌入的，如果$ d $小于$ x $的gonity。我们研究了$ {\ rm pic}^d（x）$的flat衡量标准的下拉背包的曲率。特别是，我们表明，当$ d = 1 $时，如果$ x $不是过度纤维化的，则曲率是严格的负面负数，而当$ x $是过度纤维化的时，曲率是非阳性的，并且完全消失在因$ x $的点上而消失的$ x $。
Let $X$ be a compact connected Riemann surface of genus at least two. The Abel-Jacobi map $φ: {\rm Sym}^d(X) \rightarrow {\rm Pic}^d(X)$ is an embedding if $d$ is less than the gonality of $X$. We investigate the curvature of the pull-back, by $φ$, of the flat metric on ${\rm Pic}^d(X)$. In particular, we show that when $d=1$, the curvature is strictly negative everywhere if $X$ is not hyperelliptic, and when $X$ is hyperelliptic, the curvature is nonpositive with vanishing exactly on the points of $X$ fixed by the hyperelliptic involution.
