Term for the arch supporting a gemstone

Keystone or pinnacle might be what you're looking for.

Keystone (noun): The middle stone in the top of an arch that has a special shape and holds all the other stones in position.
[Cambridge English Dictionary]

The term is not specific to jewellery and is possibly more familiar as an astrological, historical or mathematical term but those points on the crown in your picture are the apexes of cusps. Merriam Webster gives one definition (sense d in the liked entry) as

an ornamental pointed projection formed by or arising from the intersection of two arcs or foils (foil here being used in the sense of "an indentation between cusps in gothic tracery")

The entry for "cusp" also has an illustration showing a piece of ornamental tracery composed mainly of cusps.

The possibly more familiar astrological and historical uses of "cusp" are derived from sense a of the MW definition

a point of transition

(in astrology the transition from one sign or house to another)

The decorative cusp is an example of a physical cusp of which there are natural and practical examples.

The definition does not preclude the case of two convex arcs intersecting as in a pointed gothic arch but the word "cusp" is more usually applied to the intersection of concave arcs as in your crown picture.