Moduli of $\mathbb{Q}$-Gorenstein pairs and applications
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866916149746204672 |
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| author | Filipazzi, Stefano Inchiostro, Giovanni |
| author_facet | Filipazzi, Stefano Inchiostro, Giovanni |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2108_07988 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Moduli of $\mathbb{Q}$-Gorenstein pairs and applications Filipazzi, Stefano Inchiostro, Giovanni Algebraic Geometry Primary 14J10, 14D22, Secondary 14E30 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. |
| title | Moduli of $\mathbb{Q}$-Gorenstein pairs and applications |
| topic | Algebraic Geometry Primary 14J10, 14D22, Secondary 14E30 |
| url | https://arxiv.org/abs/2108.07988 |