• Corpus ID: 35183336

Jets via Hasse-Schmidt Derivations

@article{Vojta2004JetsVH,
  title={Jets via Hasse-Schmidt Derivations},
  author={Paul Vojta},
  journal={arXiv: Algebraic Geometry},
  year={2004}
}
  • Paul Vojta
  • Published 7 July 2004
  • Mathematics
  • arXiv: Algebraic Geometry
This note is intended to provide a general reference for jet spaces and jet differentials, valid in maximal generality (at the level of EGA). The approach is rather concrete, using Hasse-Schmidt (divided) higher differentials. Discussion of projectivized jet spaces (as in Green and Griffiths (1980)) is included. 
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36 Citations
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References

SHOWING 1-10 OF 18 REFERENCES

Logarithmic Jet Spaces and Extensions of de Franchis’ Theorem

Jet bundles and logarithmic 1-forms play an important role in the study of the value distribution of meromorphic mappings into algebraic varieties (cf. [01] [G-G1] and [N1∿41). On the other hand,…

Two Applications of Algebraic Geometry to Entire Holomorphic Mappings

In this paper we shall prove two theorems concerning holomorphic mappings of large open sets of ℂk into algebraic varieties. Both are in response to well-known outstanding problems, and we feel that…

Deformation quantization in algebraic geometry

The Nash problem on arc families of singularities

Nash [21] proved that every irreducible component of the space of arcs through a singularity corresponds to an exceptional divisor that appears on every resolution. He asked if the converse also…

Commutative Algebra: with a View Toward Algebraic Geometry

Introduction.- Elementary Definitions.- I Basic Constructions.- II Dimension Theory.- III Homological Methods.- Appendices.- Hints and Solutions for Selected Exercises.- References.- Index of…

The arc space of a toric variety

Algebraic approximation of structures over complete local rings

© Publications mathématiques de l’I.H.É.S., 1969, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http://…

Éléments de géométrie algébrique

© Publications mathématiques de l’I.H.É.S., 1965, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http://…

Motivic measures

© Société mathématique de France, 2002, tous droits réservés. L’accès aux archives de la collection « Astérisque » (http://smf4.emath.fr/ Publications/Asterisque/) implique l’accord avec les…

Some Investigations in the Geometry of Curve and Surface Elements