Thom's jet transversality theorem for regular maps
Thom's jet transversality theorem for regular maps
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正则地图的 Thom 射流横截定理
DOI：
10.1007/s12220-020-00515-x
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
Yuta Kusakabe
中科院分区：
文献类型：
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作者：
Yuto Sekiguchi;Mayuka Yamada;Takuya Noguchi;Chise Noomote;Mei Tsuchida;Yuki Kudoh;Yusuke Hirata;Atsushi Matsuzawa;土田芽衣;土田芽衣;土田芽衣;土田芽衣;土田芽衣;Yuta Kusakabe;Yuta Kusakabe;Yuta Kusakabe
我们建立了从仿射代数流形到满足适当柔度条件的代数流形的正则映射的Thom喷流横截定理。它可以被认为是从Stein流形到Oka流形的全纯映射的Forstneriffel喷流横截定理的代数形式。我们的喷流横截性定理意味着最大秩正则映射的一般性定理。作为一个应用，它遵循每个连通紧致局部柔性流形是一个仿射空间的全纯浸没的图像。我们还证明了在局部柔性流形中余维至少为2的每一个代数退化子簇都有Oka补。
We establish Thom’s jet transversality theorem for regular maps from an affine algebraic manifold to an algebraic manifold satisfying a suitable flexibility condition. It can be considered as the algebraic version of Forstnerič’s jet transversality theorem for holomorphic maps from a Stein manifold to an Oka manifold. Our jet transversality theorem implies genericity theorems for regular maps of maximal ranks. As an application, it follows that every connected compact locally flexible manifold is the image of a holomorphic submersion from an affine space. We also show that every algebraically degenerate subvariety of codimension at least two in a locally flexible manifold has an Oka complement.