nLab jet scheme

Idea and definition

For finite mm this is a version of mm-jet space in algebraic geometry.

Let kk be the algebraically closed field, Sch/kSch/k the category of schemes over kk and XX an object in Sch/kSch/k. The presheaf

(Sch/k) opSetY(Sch/k)(Y× kk[t]/t m+1,X) (Sch/k)^{op}\to Set\,\,\,\,\,\,\,\,\,\, Y\mapsto (Sch/k) (Y\times_k k[t]/t^{m+1},X)

is representable by a kk-scheme of finite type X mX_m the mm-jet scheme.

An analogue of the \infty-jet space is the arc space.


Readable introduction is in

  • M. Popa, 571 Ch. 5. Jet schemes and arc spaces, pdf

  • A. Beilinson, V. Drinfeld, Chiral Algebras

  • L. Ein, M. Mustaţǎ, Jet schemes and singularities, Algebraic geometry- Seattle 2005, 505–546, Proc. Sympos. Pure Math. 80, Part 2, Amer. Math. Soc., Providence, RI, 2009 MR2483946

  • L Ein, M Mustaţǎ, T Yasuda, Jet schemes, log discrepancies and inversion of adjunction, Invent. Math., 153 (2003) 519–535 math.AG/0209392

  • M Mustaţǎ, Jet schemes of locally complete intersection canonical singularities, with an appendix by David Eisenbud and Edward Frenkel, Invent. Math., 145 (2001) 397–424; Singularities of pairs via jet schemes, J. Amer. Math. Soc., 15 (2002) 599–615

Last revised on October 24, 2022 at 23:42:50. See the history of this page for a list of all contributions to it.