MODULI OF Q-GORENSTEIN PAIRS AND APPLICATIONS

We develop a framework to construct moduli spaces of Q-Gorenstein pairs. To do so, we fix certain invariants; these choices are encoded in the notion of Q-stable pair. We show that these choices give a proper moduli space with projective coarse moduli space and they prevent some pathologies of the moduli space of stable pairs when the coefficients are smaller than 21. Lastly, we apply this machinery to provide an alternative proof of the projectivity of the moduli space of stable pairs.