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Demailly-Semple jets in dimension 3. (Étude des jets de Demailly-Semple en dimension 3.) (French) Zbl 1092.58003
The author presents an algebraic characterization of Demailly-Semple jets in dimension $$3$$ by using the invariant theory of non reductive groups. In dimension $$3$$, the algebra of differential operators is generated by the first order jets $$f^\prime_i$$, the expressions $$w_{ij}=f^\prime_if^{\prime \prime}_j-f^\prime_jf^{\prime \prime}_i$$ involving jets of first and second order, some expressions $$w^k_{ij}$$ involving jets of first, second and third order and a determinant $$W$$ defined by the jets of first, second and third order of the components $$f_1,f_2,f_3$$. The degree is $$7$$. The main geometric applications consist in the characterization of the graded bundle of jets of order $$3$$ on a three-dimensional complex manifold and in the computation of the Euler-Poincaré characteristic of a smooth hypersurface of degree $$d$$ in $$\mathbb{P}^4$$.

##### MSC:
 58A20 Jets in global analysis 32Q45 Hyperbolic and Kobayashi hyperbolic manifolds 13A50 Actions of groups on commutative rings; invariant theory 06B05 Structure theory of lattices
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##### References:
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