Modulador FM

What role does C2 play? I understand C1 adds feedback input(causing current oscillations in transistor), but wonder how C2 makes the voltage oscillations happen?

hmmm, may be should i see this as Colpitts Oscillator(C1,C2 L1) feeding in at the emitter and feedback at collector, with a runtime trimmer modulator capacitor on BC547(miller capacitance).

still wonder how to factor in C3 at resonance frequency.