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Belghitti-Gruson or Semple?

In: Algebra, Arithmetic and Geometry with Applications

Author

Listed:
  • Vincent Cossart

Abstract

In this short note, we want to make some advertising for two spaces one defined by Semple in [S], the other by Belghitti and Gruson in [B]. The the n-th Semple’s tower over X is the smallest space where you can realize the set of all sequences of length n of Nash’s blowing-ups of curves embedded in X, the n-th Belghitti-Gruson’s space parametrizes the set of sequences of length n of blowingups centered at near closed points of X. The existence of such spaces is interesting by itself, and good descriptions (whatever it means) of them would be full of informations. The constructions of these spaces are a priori quite different. We show that, in fact, they are quite similar and closely related: they have the same Chow ring. In this note, X is a regular irreducible scheme over an algebraic closed field k. A curve in an ambient space is a closed reduced irreducible subscheme of dimension 1 of the ambient space.

Suggested Citation

  • Vincent Cossart, 2004. "Belghitti-Gruson or Semple?," Springer Books, in: Chris Christensen & Avinash Sathaye & Ganesh Sundaram & Chandrajit Bajaj (ed.), Algebra, Arithmetic and Geometry with Applications, pages 259-262, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-18487-1_14
    DOI: 10.1007/978-3-642-18487-1_14
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