Finite-dimensionality criterion for local Picard groups of S2 surfaces

Let (s,S)(s,S) be an S2S_2 surface. Finite-dimensionality conjecture. There is a finite-dimensional local Picard group Picloc(s,S)\operatorname{\mathbf{Pic}}^{\rm loc}(s,S) if and only if SS is seminormal. The conjecture is motivated by the contrast between normal complex surface singularities, where finite-dimensional local Picard groups are known, and many non-normal examples in which no finite-dimensional local Picard group exists; its resolution is not supplied in the source.

Sources & referencesView supporting material

Primary source

János Kollár, “Maps between local Picard groups”, arXiv:1407.5108 (2014).

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