摘要翻译：
给出了非负Kodaira维数光滑射影曲面S$上所有具有常几何亏格G\geq2$和超椭圆正规化的曲线族的存在性限制。特别地，我们证明了一个Reider-like结果，它的证明是“无向量丛”，并依赖于形变理论和有理曲线的弯曲与断裂。我们也给出了这类曲线族的例子。
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英文标题：
《Remarks on families of singular curves with hyperelliptic normalizations》
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作者：
Andreas Leopold Knutsen
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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：
  We give restrictions on the existence of families of curves on smooth projective surfaces $S$ of nonnegative Kodaira dimension all having constant geometric genus $g \geq 2$ and hyperelliptic normalizations. In particular, we prove a Reider-like result whose proof is ``vector bundle-free'' and relies on deformation theory and bending-and-breaking of rational curves in $\Sym^2(S)$. We also give examples of families of such curves.
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PDF链接：
https://arxiv.org/pdf/0705.0906