Moduli of $\mathbb{Q}$-Gorenstein pairs and applications

Abstract

We develop a framework to construct moduli spaces of $\mathbb{Q}$-Gorenstein pairs. To do so, we fix certain invariants; these choices are encoded in the notion of $\mathbb{Q}$-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 $\frac{1}{2}$. Lastly, we apply this machinery to provide an alternative proof of the projectivity of the moduli space of stable pairs.

Improved exposition and minor corrections throughout. Final version to appear in Journal of Algebraic Geometry

References in corpus (2)

• Moduli of varieties of general type
• Moduli of algebraic varieties

Cited by in corpus (2)

• Complements and coregularity of Fano varieties
• On semi-ampleness of the moduli part