adv

Chern scalar curvature and symmetric products of compact Riemann surfaces. (arXiv:1804.04524v1 [math.DG])

来源于:arXiv
Let $X$ be a compact connected Riemann surface of genus $g\geq 0$, and let ${\rm Sym}^d(X)$, $d \ge 1$, denote the $d$-fold symmetric product of $X$. We show that ${\rm Sym}^d(X)$ admits a Hermitian metric with negative Chern scalar curvature if and only if $g \geq 2$, and positive Chern scalar curvature if and only if $d > g$. 查看全文>>