nLab locus

Idea

In mathematics, by a locus one typically means a kind of subspace of points satisfying some prescribed conditions.

For example:

• a critical locus is a subspace of critical points in the domain of a differentiable function;

• a fixed locus is a subspace of fixed points under a group action;

• the term algebraic locus is sometimes used (e.g. Moerdijk Reyes 1991, p. 8 or arXiv:1604.07827, p. 1-2) for what more commonly are called varieties, namely subspaces of solutions to polynomial equations;

  similarly, there is a notion of smooth locus.

Unrelated entries

Un-related to this standard use of “locus” is the notion of Joyal locus in (higher) topos theory.

References

See also

• Wikipedia, Locus (mathematics)