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摘要翻译：
设p:c-->y是光滑射影曲线的覆盖，它是2次的\pi:c-->c'和n次的g:c'-->y的合成。设F:x-->y是2^n次的覆盖，其中曲线X是G:c′-->y的纤维在C^{(n)}中的提升量的参数。设P(X，\delta)是相关的Prym-Tyurin变种，已知与Prym变种P(C，C')同生。本文的大部分结果集中在计算JX的正则极化对P（X,\delta)约束的极化类型上。我们得到了n=3时的偏振类型。当y=P^1时，我们猜想P(X,\delta)与Prym簇P(C,C′)的对偶同构。当n=2时这是已知的，当n=3时我们证明了这一点，对于任意n来说，如果\pi:c-->c'是\'{e}故事。对于其他一些类型的覆盖也得到了类似的结果。
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英文标题：
《Polarization types of isogenous Prym-Tyurin varieties》
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作者：
Vassil Kanev, Herbert Lange
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最新提交年份：
2007
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
Let p:C-->Y be a covering of smooth, projective curves which is a composition of \pi:C-->C' of degree 2 and g:C'-->Y of degree n. Let f:X-->Y be the covering of degree 2^n, where the curve X parametrizes the liftings in C^{(n)} of the fibers of g:C'-->Y. Let P(X,\delta) be the associated Prym-Tyurin variety, known to be isogenous to the Prym variety P(C,C'). Most of the results in the paper focus on calculating the polarization type of the restriction of the canonical polarization of JX on P(X,\delta). We obtain the polarization type when n=3. When Y=P^1 we conjecture that P(X,\delta) is isomorphic to the dual of the Prym variety P(C,C'). This was known when n=2, we prove it when n=3, and for arbitrary n if \pi:C-->C' is \'{e}tale. Similar results are obtained for some other types of coverings.
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PDF链接：
https://arxiv.org/pdf/0707.0364
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