higher geometry / derived geometry
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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.
Un-related to this standard use of “locus” is the notion of Joyal locus in (higher) topos theory.
See also
Last revised on July 20, 2022 at 07:25:59. See the history of this page for a list of all contributions to it.