摘要翻译：
本文研究了射影空间中的三重X,该射影空间的超平面截面是一个光滑的椭圆纤维曲面。我们首先给出了Picard数为2的曲面可能嵌入的一般定理。更精确的结果，然后证明了Weierstrass纤维，两个等级和更高。特别地，我们证明了非K3曲面的二阶Weierstrass纤维不是局部完全交集三重的超平面截面，并给出了任意阶Weierstrass纤维的许多嵌入必须是锥的条件。
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英文标题：
《On the extendability of elliptic surfaces of rank two and higher》
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作者：
Angelo Felice Lopez, Roberto Munoz and Jose' Carlos Sierra
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最新提交年份：
2008
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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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一级分类：Mathematics        数学
二级分类：Commutative Algebra        交换代数
分类描述：Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics
交换环，模，理想，同调代数，计算方面，不变理论，与代数几何和组合学的联系
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英文摘要：
  We study threefolds X in a projective space having as hyperplane section a smooth surface with an elliptic fibration. We first give a general theorem about the possible embeddings of such surfaces with Picard number two. More precise results are then proved for Weierstrass fibrations, both of rank two and higher. In particular we prove that a Weierstrass fibration of rank two that is not a K3 surface is not hyperplane section of a locally complete intersection threefold and we give some conditions, for many embeddings of Weierstrass fibrations of any rank, under which every such threefold must be a cone.
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PDF链接：
https://arxiv.org/pdf/0806.1440