Luminosity and beam-beam tune shifts with crossing angle and hourglass effects in e${}^{+}$-e${}^{-}$ colliders

We develop theoretical expressions for the luminosity and beam-beam tune shifts in the presence of both a crossing angle and hourglass effects for the present and next generation of symmetric e${}^{+}$-e${}^{-}$ colliders. The theory is applied to the design of the Fermilab site filler Higgs factory and to the FCC-ee collider.