  An enduring question in correlated systems concerns whether superconductivity
is favoured at a quantum critical point (QCP) characterised by a divergent
quasiparticle effective mass. Despite such a scenario being widely postulated
in high Tc cuprates and invoked to explain non-Fermi liquid transport
signatures, experimental evidence is lacking for a critical divergence under
the superconducting dome. We use ultra-strong magnetic fields to measure
quantum oscillations in underdoped YBa2Cu3O6+x, revealing a dramatic
doping-dependent upturn in quasiparticle effective mass at a critical
metal-insulator transition beneath the superconducting dome. Given the location
of this QCP under a plateau in Tc in addition to a postulated QCP at optimal
doping, we discuss the intriguing possibility of two intersecting
superconducting subdomes, each centred at a critical Fermi surface instability.
