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Let $X$ be an equidimensional variety of dimension $n$ over a field that can be covered by open subvarieties of certain intersections of $N-n$ hypersurfaces in $P^N$ (for a large enough $N$; we consider set-theoretic intersections). Then $X$ can be called locally a set-theoretic complete intersection; this term sounds poorly and does not seem to be standard.

Is there a better term? How would you call $X$ if it is locally an intersection of $N-n+c$ hypersurfaces in $P^N$?

Upd. What do you think about "(locally?) requires only $c$ extra equations"?

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    $\begingroup$ Personally, I would say "set-theoretically local complete intersection." Since people abbreviate "local complete intersection" as "LCI", you might abbreviate this as "stLCI". $\endgroup$
    – Jason Starr
    Commented Dec 21, 2014 at 11:57
  • $\begingroup$ Why not "STLCI"?:) Previously I wrote "LSTCI" instead. Was any abbreviation of this sort used in literature? $\endgroup$
    – Mikhail Bondarko
    Commented Dec 21, 2014 at 15:12
  • $\begingroup$ I haven't seen a name for it either. $\endgroup$
    – Karl Schwede
    Commented Dec 22, 2014 at 4:44

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