Fuel-injection device in a turbomachine

A fuel injection device in a turbomachine, comprising:

• at least one pump connecting a fuel tank to flow rate control means supplying fuel injectors through the intermediary of a pressurization and cut-off valve, said valve comprising
• a piston that can be moved inside a cylindrical body between a closed position and an open position for feeding the injectors,
• means for applying the fuel pressure at the flow rate control means to the piston for closing the injector supply as long as said fuel pressure is lower than a first predetermined threshold, and
• means for applying a counter-pressure on the piston for closing the injector supply, as from the idle speed of the turbomachine, thereby creating a second pressurization threshold, such second threshold exceeding the first threshold and a minimal pressure value for controlling equipment with variable geometry of the turbomachine,
• wherein the cylindrical body of the valve comprises an orifice connected to the inlet of the pump, this orifice being axially spaced away from the means for applying the counter-pressure defining the second pressurization threshold, in order to permanently apply a pressure at the pump inlet on the piston and to define the first pressurization threshold.