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arXiv · 2108.07988

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

Stefano Filipazzi·Giovanni Inchiostro
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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.

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Stefano Filipazzi, Giovanni Inchiostro. 2021-08-18. Moduli of $\mathbb{Q}$-Gorenstein pairs and applications. https://doi.org/10.1090/jag/823

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