  The transition temperature Tc of cuprate superconductors falls when the
doping p is reduced below a certain optimal value. It is unclear whether this
fall is due to strong phase fluctuations or to a decrease in the pairing gap.
Different interpretations of photoemission data disagree on the evolution of
the pairing gap and different estimates of the upper critical field Hc2 are in
sharp contradiction. Here we resolve this contradiction by showing that
superconducting fluctuations in the underdoped cuprate Eu-LSCO, measured via
the Nernst effect, have a characteristic field scale that falls with
underdoping. The critical field Hc2 dips at p = 0.11, showing that
superconductivity is weak where stripe order is strong. In the archetypal
cuprate superconductor YBCO, Hc2 extracted from other measurements has the same
doping dependence, also with a minimum at p = 0.11, again where stripe order is
present. We conclude that competing states such as stripe order weaken
superconductivity and this, rather than phase fluctuations, causes Tc to fall
as cuprates become underdoped.
