Orbifold splice quotients and log covers of surface pairs
| Autor: | Neumann, Walter D., Wahl, Jonathan |
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| Rok vydání: | 2020 |
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| Zdroj: | Journal of Singularities, Vol. 23 (2021), 151-169 |
| Druh dokumentu: | Working Paper |
| Popis: | A three-dimensional orbifold $(\Sigma, \gamma_i, n_i)$, where $\Sigma$ is a rational homology sphere, has a universal abelian orbifold covering, whose covering group is the first orbifold homology. A singular pair $(X,C)$, where $X$ is a normal surface singularity with $\mathbb Q$HS link and $C$ is a Weil divisor, gives rise on its boundary to an orbifold. One studies the preceding orbifold notions in the algebro-geometric setting, in particular defining the universal abelian log cover of a pair. A first key theorem computes the orbifold homology from an appropriate resolution of the pair. In analogy with the case where $C$ is empty and one considers the universal abelian cover, under certain conditions on a resolution graph one can construct pairs and their universal abelian log covers. Such pairs are called orbifold splice quotients. Comment: 22 pages;referee remarks incorporated; definitions of "orbifold" and "singular pair" contrasted with alternative usage of terms; algebro-geometric proof of existence of UALC (Theorem 3.1); Section 7 example corrected |
| Databáze: | arXiv |
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