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摘要翻译：
虽然等量曲线族的切空间可以用扭曲理想束的截面来区分，但如果我们只规定一个奇点应该具有的重数，这就不再成立了。然而，借助于等多性理想，仍有可能计算切空间的维数。本文考虑光滑射影曲面S上具有固定正整数m的线性系统L中具有C的族L_m={（C,p）mult_p(C)=m},并根据p是否为C的单程奇点，计算了L_m在点（C,p）处的切空间的维数。我们推导出L_m在（C,p）处的期望维数为diml+2-m*(m+1)/2。这一结果在与Luca Chiantini的一些联合论文中用于三点缺陷曲面的研究。
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英文标题：
《A Note on Equimultiple Deformations》
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作者：
Thomas Markwig
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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：
While the tangent space to an equisingular family of curves can be discribed by the sections of a twisted ideal sheaf, this is no longer true if we only prescribe the multiplicity which a singular point should have. However, it is still possible to compute the dimension of the tangent space with the aid of the equimulitplicity ideal. In this note we consider families L_m={(C,p) | mult_p(C)=m} with C in some linear system |L| on a smooth projective surface S and for a fixed positive integer m, and we compute the dimension of the tangent space to L_m at a point (C,p) depending on whether p is a unitangential singular point of C or not. We deduce that the expected dimension of L_m at (C,p) in any case is just dim|L|+2-m*(m+1)/2. The result is used in the study of triple-point defective surfaces in some joint papers with Luca Chiantini.
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PDF链接：
https://arxiv.org/pdf/0705.3911
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