Abstract
This chapter is devoted to the theory of jet spaces and jet differentials. The idea of using differential equations in hyperbolicity problems can be traced back to work of Bloch [7]. The modern language adopted here has been initiated by [31] and later refined by several authors, such as [17] and [55]. We shall describe the construction of the vector bundle of jet differentials and explain how to build in a functorial way a tower of projective bundles together with the corresponding tautological line bundles on any given manifold which provides a relative compactification of the classical jets spaces. Then, a characterization of jet differentials in terms of direct images of these tautological line bundles will be given.
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Diverio, S., Rousseau, E. (2016). Jets spaces. In: Hyperbolicity of Projective Hypersurfaces. IMPA Monographs, vol 5. Springer, Cham. https://doi.org/10.1007/978-3-319-32315-2_3
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DOI: https://doi.org/10.1007/978-3-319-32315-2_3
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