差可
Abel–Jacobi map and curvature of the pulled back
metric
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期刊名称： Bulletin of Mathematical Sciences
我的驾校教练作者： Indranil Biswas六级题目
年份： 2020年
男性阴部关键词： Gonality;curvature;symmetric productAbel–Jacobi map
科技内容
玩具市场摘要：Let X X X be a compact connected Riemann surface of genus at least two. The Abel-Jacobi map \\varphi: {m Sym}^d(X) ightarrow {m Pic}^d(X) \\varphi: {m Sym}^d(X) ightarrow {m Pic}^d(X) is an embedding if d d is less than the gonality of X X . We investigate the curvature of the pull-back, by \\varphi \\varphi , of the flat metric on {m Pic}^d(X) {m Pic}^d(X) . In particular, we show that when d=1 d=1 , the curvature is strictly negative everywhere if X X is not hyperelliptic, and when X X is hyperelliptic, the curvature is nonpositive with vanishing exactly on the points of X X fixed by the hyper
elliptic involution.
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