A simple characteristic-free proof of the Brill-Noether theorem
A simple characteristic-free proof of the Brill-Noether theorem
复制标题
布里尔-诺特定理的简单无特征证明
DOI：
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发表时间：
2011
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影响因子：
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通讯作者：
Brian Osserman
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文献类型：
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作者：
Brian Osserman
在welters之后，我们描述了如何使用与Eisenbud和Harris所考虑的退化不同的退化来使用极限线性级数来证明Brill-Noether定理的一个简单且与特征无关的证明。根据退化，我们证明了定理的扩展版本，允许在最多两点上施加分支。虽然该领域的专家早就知道主要思想，但我们解决了在证明定理完整版本时出现的一些技术问题。
FollowingWelters, we describe howthe use of a different degeneration from that considered by Eisenbud and Harris leads to a simple and characteristic-independent proof of the Brill-Noether theorem using limit linear series. As suggested by the degeneration, we prove an extended version of the theorem allowing for imposed ramification at up to two points.Although experts in the field have long been aware of themain ideas, we address some technical issues which arise in proving the full version of the theorem.