On k-Jet Ampleness

摘要: Let X be an n-dimensional projective manifold mapped into a space Ψ:X → ℙℂ. L the pullback, Ψ*Oℙℂ(1), of hyperplane section bundle. If Ψ is embedding, said to very ample. This intensively studied and well-understood concept. In this chapter we study particular notion higher-order embedding. We say that k-jet ample for nonnegative integer k if, given any r integers 1 , ., such \( + = \sum\nolimits_{i 1}^r {{k_i}} \) distinct points {x ,. . x } ⊂ X, evaluation map $$ \times \Gamma (L) \to L/L \otimes m_{{x_1}}^{{k_1}} ... m_{xr}^{{k_r}} 0 $$ is surjective, where m xi denotes maximal ideal at t Note spanned (respectively, ample) if only 0-jet 1-jet ample).