  Cosmological neutrinos have their greatest influence in voids: these are the
regions with the highest neutrino to dark matter density ratios. The marked
power spectrum can be used to emphasize low density regions over high density
regions, and therefore is potentially much more sensitive than the power
spectrum to the effects of neutrino masses. Using 22,000 N-body simulations
from the Quijote suite, we quantify the information content in the marked power
spectrum of the matter field, and show that it outperforms the standard power
spectrum by setting constraints improved by a factor larger than 2 on all
cosmological parameters. The combination of marked and standard power spectrum
allows to place a 4.3{\sigma} constraint on the minimum sum of the neutrino
masses with a volume equal to 1 (Gpc/h)^3 and without CMB priors. Combinations
of different marked power spectra yield a 6{\sigma} constraint within the same
conditions.
