Local volumes, equisingularity, and generalized smoothability
Local volumes, equisingularity, and generalized smoothability
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局部体积、等奇异性和广义平滑性
DOI：
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
Antoni Rangachev
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文献类型：
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作者：
Antoni Rangachev
我们引入了一个相对非常充分的可逆层的限制局部体积作为不变的equisingularity通过确定其跨家庭的变化。我们应用这一结果给Whitney-Thom（微分）equisingularity的孤立的复杂的解析奇点的家庭的数字控制。局部体积的消失的表征产生了一类缺陷余法（DC）奇点。我们引入了广义光滑性的概念，通过考虑一类奇异变形为直流奇点。利用Whitney分层和余正规空间的函性性质，我们证明了余正规空间的纤维在横映射下表现良好。然后利用Thom的横截性、Hilbert-Burch和Buchsbaum-Eisenbud的结构定理，证明了所有维数至少为2，Cohen-Macaulay余维数为2，Gorenstein余维数为3的可光滑奇点，以及更一般的行列式奇点和Pfenstein奇点都变形为dc奇点。
We introduce the restricted local volume of a relatively very ample invertible sheaf as an invariant of equisingularity by determining its change across families. We apply this result to give numerical control of Whitney-Thom (differential) equisingularity for families of isolated complex analytic singularities. The characterization of the vanishing of the local volume gives rise to the class of deficient conormal (dc) singularities. We introduce a notion of generalized smoothability by considering the class of singularities that deform to dc singularities. Using Whitney stratifications and the functoriality properties of conormal spaces we show that fibers of conormal spaces are well-behaved under transverse maps. Then by Thom's transversality, the structure theorems of Hilbert-Burch and Buchsbaum-Eisenbud, we show that all smoothable singularities of dimension at least 2, Cohen-Macaulay codimension 2, Gorenstein codimension 3, and more generally determinantal and Pfaffian singularities deform to dc singularities.
DOI：
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发表时间：
2006
期刊：
Integrable systems, geometry, and topology, AMS/IP Studies of Advanced Mathematics, American Mathematical Society 36
影响因子：
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作者：
FURUYA;Jun;Martin Guest
通讯作者：
Martin Guest