论文标题
部分呈现
Partial desingularization
论文作者
论文摘要
我们解决了以下局部降低的问题，以保留正常的横梁。给定特征为零的代数（或分析）品种X，我们是否可以找到有限的爆破序列，以保留X的正常交叉基因座，此后，X的变换X X'仅来自明确的有限有限列表的奇异列表，我们使用循环矩阵的确定性来定义了最小的奇异性列表。例如，在表面上，捏点或惠特尼伞是正常穿越之外所需的唯一奇异性。 我们开发了具有规则（或分析）系数的一元多项式分解（分裂）的技术，满足了通用正常交叉假设，我们将其与奇异性技术的分辨率一起使用，以找到局部循环正常形式的奇异性。这些技术处于当前状态足以对上述问题，DIM X的正面答案，最多为4，或者在任意维度上，如果我们仅保留最多三个订单的正常横梁。在这些情况下，最小的奇异性具有平稳的归一化。
We address the following question of partial desingularization preserving normal crossings. Given an algebraic (or analytic) variety X in characteristic zero, can we find a finite sequence of blowings-up preserving the normal-crossings locus of X, after which the transform X' of X has only singularities from an explicit finite list of minimal singularities, which we define using the determinants of circulant matrices. In the case of surfaces, for example, the pinch point or Whitney umbrella is the only singularity needed in addition to normal crossings. We develop techniques for factorization (splitting) of a monic polynomial with regular (or analytic) coefficients, satisfying a generic normal crossings hypothesis, which we use together with resolution of singularities techniques to find local circulant normal forms of singularities. These techniques in their current state are enough for a positive answer to the question above, for dim X up to 4, or in arbitrary dimension if we preserve normal crossings only of order at most three. In these cases, minimal singularities have smooth normalization.
