Geodesic
Orbifold splice quotients and log covers of surface pairs
Journal of Singularities, Tome 23 (2021), pp. 151-169

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A three-dimensional orbifold (Σ, γ_i, n_i)$, where Σ 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 QHS 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, proving the existence of the universal abelian log cover of a pair. A 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.
DOI : 10.5427/jsing.2021.23i
Classification : 32S50, 14J17, 57M25, 57N10 
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     author = {Walter D. Neumann and Jonathan Wahl},
     title = {Orbifold splice quotients and log covers of surface pairs},
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     pages = {151--169},
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     volume = {23},
     year = {2021},
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Walter D. Neumann; Jonathan Wahl. Orbifold splice quotients and log covers of surface pairs. Journal of Singularities, Tome 23 (2021), pp. 151-169. doi: 10.5427/jsing.2021.23i

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