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摘要翻译：
本文利用Viro拼接方法，提出了一种构造实平面分支$(C，0)$光滑的新方法。由于实平面分支一般都是牛顿退化的，因此不能直接应用Viro拼接法。相反，我们对某些具有多个分支的牛顿非退化曲线奇点应用了拼接方法。这些奇点是分支的严格变换在奇点的toric内嵌分辨率为$(C，0)$的无穷近点处迭代变形的结果。我们用局部数据对该方法得到的$M$-平滑进行了表征。特别地，我们分析了一类多重Harnack光顺，这些光顺是由(C，0)的严格变换相对于坐标线处于最大位置的序列的M-光顺引起的。证明了多Harnack光滑的拓扑类型是唯一的，它是由分支的复等性类型决定的。这一结果是Mikhalkin最近一个定理的局部版本。
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英文标题：
《Multi-Harnack smoothings of real plane branches》
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作者：
Pedro Daniel Gonzalez Perez (DPTO. ALGEBRA UCM), Jean-Jacques Risler
(IMJ)
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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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英文摘要：
We introduce a new method for the construction of smoothings of a real plane branch $(C, 0)$ by using Viro Patchworking method. Since real plane branches are Newton degenerated in general, we cannot apply Viro Patchworking method directly. Instead we apply the Patchworking method for certain Newton non degenerate curve singularities with several branches. These singularities appear as a result of iterating deformations of the strict transforms of the branch at certain infinitely near points of the toric embedded resolution of singularities of $(C,0)$. We characterize the $M$-smoothings obtained by this method by the local data. In particular, we analyze the class of multi-Harnack smoothings, those smoothings arising in a sequence $M$-smoothings of the strict transforms of (C,0) which are in maximal position with respect to the coordinate lines. We prove that there is a unique the topological type of multi-Harnack smoothings, which is determined by the complex equisingularity type of the branch. This result is a local version of a recent Theorem of Mikhalkin.
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PDF链接：
https://arxiv.org/pdf/0808.0157
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