The Torelli map restricted to the hyperelliptic locus

Transactions of the American Mathematical Society, Series B Pub Date : 2019-11-05 DOI:10.1090/BTRAN/64

Aaron Landesman

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引用次数: 7

Abstract

Let g ≥ 2 g \geq 2 and let the Torelli map denote the map sending a genus g g curve to its principally polarized Jacobian. We show that the restriction of the Torelli map to the hyperelliptic locus is an immersion in characteristic not 2 2 . In characteristic 2 2 , we show the Torelli map restricted to the hyperelliptic locus fails to be an immersion because it is generically inseparable; moreover, the induced map on tangent spaces has kernel of dimension g − 2 g-2 at every point.

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托雷利图局限于超椭圆轨迹

设g≥2g \geq 2，并设Torelli映射表示将g属曲线发送到其主极化雅可比矩阵的映射。我们证明了Torelli映射对超椭圆轨迹的限制是对特征非22的浸没。在特征22中，我们证明了局限于超椭圆轨迹的Torelli映射不能成为浸没，因为它是一般不可分的;此外，切空间上的诱导映射在每一点上都具有g−2 g-2维核。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Transactions of the American Mathematical Society, Series B

CiteScore

1.70

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0.00%

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