Isomorphisms of jet schemes

Details Isomorphisms of jet schemes Isomorphisms of jet schemes

2009-08-08

arxiv.org/abs/0908.1146v1

Mathematics

Algebraic Geometry

6 pages, to appear in Canadian Comptes Rendus

Scientific paper

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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