  The occurrence of planetary nebulae (PNe) in globular clusters (GCs) provides
an excellent chance to study low-mass stellar evolution in a special
(low-metallicity, high stellar density) environment. We report a systematic
spectroscopic survey for the [O{\sc iii}] 5007 emission line of PNe in 1469
Virgo GCs and 121 Virgo ultra-compact dwarfs (UCDs), mainly hosted in the giant
elliptical galaxies M87, M49, M86, and M84. We detected zero PNe in our UCD
sample and discovered one PN ($M_{5007} = -4.1$ mag) associated with an M87 GC.
We used the [O{\sc iii}] detection limit for each GC to estimate the
luminosity-specific frequency of PNe, $\alpha$, and measured $\alpha$ in the
Virgo cluster GCs to be $\alpha \sim 3.9_{-0.7}^{+5.2}\times
10^{-8}\mathrm{PN}/L_\odot$. $\alpha$ in Virgo GCs is among the lowest values
reported in any environment, due in part to the large sample size, and is 5--6
times lower than that for the Galactic GCs. We suggest that $\alpha$ decreases
towards brighter and more massive clusters, sharing a similar trend as the
binary fraction, and the discrepancy between the Virgo and Galactic GCs can be
explained by the observational bias in extragalactic surveys toward brighter
GCs. This low but non-zero efficiency in forming PNe may highlight the
important role played by binary interactions in forming PNe in GCs. We argue
that a future survey of less massive Virgo GCs will be able to determine
whether PN production in Virgo GCs is governed by internal process (mass,
density, binary fraction), or is largely regulated by external environment.
