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Bibliographic Details
Main Author: Halic, Mihai
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2401.16196
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author Halic, Mihai
author_facet Halic, Mihai
contents The G3-property of a subvariety was introduced by Hironaka-Matsumura, and plays an important role for deducing connectedness and extension results. Unfortunately, it's a rather elusive notion, which is not always easy to establish. Most of the existing work is concentrated on subvarieties of homogeneous varieties. The first goal of this article is to show that mobility assumptions on the subvariety, considered in works of Badescu, Chow, Debarre, Voisin, yield a certain partial positivity property, slightly stronger than G3, previously introduced by the author. Second, we apply the result to prove that, in numerous situations, the splitting of the normal bundle of a smooth two-codimensional subvariety implies that it is a complete intersection.
format Preprint
id arxiv_https___arxiv_org_abs_2401_16196
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle G3-Criteria and Applications
Halic, Mihai
Algebraic Geometry
14C25, 14B20, 14M10, 14M17
The G3-property of a subvariety was introduced by Hironaka-Matsumura, and plays an important role for deducing connectedness and extension results. Unfortunately, it's a rather elusive notion, which is not always easy to establish. Most of the existing work is concentrated on subvarieties of homogeneous varieties. The first goal of this article is to show that mobility assumptions on the subvariety, considered in works of Badescu, Chow, Debarre, Voisin, yield a certain partial positivity property, slightly stronger than G3, previously introduced by the author. Second, we apply the result to prove that, in numerous situations, the splitting of the normal bundle of a smooth two-codimensional subvariety implies that it is a complete intersection.
title G3-Criteria and Applications
topic Algebraic Geometry
14C25, 14B20, 14M10, 14M17
url https://arxiv.org/abs/2401.16196