Abel–Jacobi map and curvature of the pulled back metric
Let [Formula: see text] be a compact connected Riemann surface of genus at least two. The Abel–Jacobi map [Formula: see text] is an embedding if [Formula: see text] is less than the gonality of [Formula: see text]. We investigate the curvature of the pull-back, by [Formula: see text], of the flat metric on [Formula: see text]. In particular, we show that when [Formula: see text], the curvature is strictly negative everywhere if [Formula: see text] is not hyperelliptic, and when [Formula: see text] is hyperelliptic, the curvature is nonpositive with vanishing exactly on the points of [Formula: see text] fixed by the hyperelliptic involution.
2009 ◽
Vol 20
(08)
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pp. 1069-1080
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2013 ◽
Vol 50
(1)
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pp. 31-50
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2011 ◽
Vol 26
(26)
◽
pp. 4647-4660
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