On jet closures of singularities

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Abstract

Jet closure and jet support closure were first introduced by de Fernex, Ein and Ishii to solve the local isomorphism problem. In this paper we introduce two local algebras associated to jet closure and jet support closure, respectively. We show that these two algebras are invariants of singularities. We compute and investigate these invariants for some interesting cases, such as the cases of monomial ideals and homogeneous ideals. For application, we can distinguish different simple curve singularities by a finite number of jet support closures, and this number is close to the Milnor number of the singularity. We also introduce a new filtration and a jet index for jet closures. The jet index describes which jet scheme recovers the information on the base scheme. Moreover, we obtain some properties of the jet index. Bibliography: 16 titles.

About the authors

Yifan Chen

Department of Mathematical Sciences, Tsinghua University, Beijing, P. R. China

Author for correspondence.
Email: c-yf20@tsinghua.org.cn

Huaiqing Zuo

Department of Mathematical Sciences, Tsinghua University, Beijing, P. R. China

Email: hqzuo@mail.tsinghua.edu.cn

References

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