Kavli Affiliate: Alexey Bondal
| Summary:
We define a normal surface $X$ to be codim-2-saturated if any open embedding of $X$ into a normal surface with the complement of codimension 2 is an isomorphism. We show that any normal surface $X$ allows a codim-2-saturated model $widehatX$ together with the canonical open embedding $Xto widehatX$.
Any normal surface which is proper over its affinisation is codim-2-saturated, but the converse does not hold. We give a criterion for a surface to be codim-2-saturated in terms of its Nagata compactification and the boundary divisor.
We reconstruct the codim-2-saturated model of a normal surface $X$ from the additive category of reflexive sheaves on $X$. We show that the category of reflexive sheaves on $X$ is quasi-abelian and we use its canonical exact structure for the reconstruction.
In order to deal with categorical issues, we introduce a class of weakly localising Serre subcategories in abelian categories. These are Serre subcategories whose categories of closed objects are quasi-abelian. This general technique might be of independent interest.
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