Belghitti-Gruson or Semple?

Vincent Cossart

A chapter in Algebra, Arithmetic and Geometry with Applications, 2004, pp 259-262 from Springer

Abstract: 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.

Keywords: Exact Sequence; Vector Bundle; Ambient Space; Exceptional Divisor; Chow Ring (search for similar items in EconPapers)
Date: 2004
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-18487-1_14

Ordering information: This item can be ordered from
http://www.springer.com/9783642184871

DOI: 10.1007/978-3-642-18487-1_14

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().