2021
DOI: 10.48550/arxiv.2105.08749
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Local volumes, equisingularity, and generalized smoothability

Antoni Rangachev

Abstract: 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 o… Show more

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