The subset of the unmarked moduli space of Riemann surfaces with hyperbolic systole at least is compact for fixed genus . Use a Bers pants decomposition theorem bound, finitely many topological decomposition types and Dehn twists to place representatives in finitely many compact boxes in Fenchel–Nielsen coordinates.
Articles by others on the same topic
Mumford's compactness theorem is a result in algebraic geometry that pertains to the study of families of algebraic curves. Specifically, it provides conditions under which a certain space of algebraic curves can be compactified. The theorem states that the moduli space of stable curves of a given genus \( g \) (the space that parameterizes all algebraic curves of that genus, up to certain equivalences) is compact.