Geodesic
On jet closures of singularities
Sbornik. Mathematics, Tome 216 (2025) no. 1, pp. 99-131

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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.
Keywords: jet closure, jet support closure
Mots-clés : filtration. 
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Y. Chen; H. Zuo. On jet closures of singularities. Sbornik. Mathematics, Tome 216 (2025) no. 1, pp. 99-131. http://geodesic.mathdoc.fr/item/SM_2025_216_1_a5/