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arXiv · 0908.1146

Isomorphisms of jet schemes

Shihoko Ishii·Joerg Winkelmann
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Abstract

If two schemes are isomorphic, then their $m$-jet schemes are isomorphic for all $m$. In this paper we consider the converse problem. We prove that if an isomorphism of the $m$-jet schemes is induced from a morphism of the base schemes, then the morphism of the base schemes is an isomorphism. But we also prove that just the existence of isomorphisms between $m$-jet schemes does not yield the existence of an isomorphism between the base schemes.

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Shihoko Ishii, Joerg Winkelmann. 2009-08-08. Isomorphisms of jet schemes. https://arxiv.org/abs/0908.1146

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