Kavli Affiliate: Alexey Bondal
| First 5 Authors: Agnieszka Bodzenta, 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 $widehat{X}$ together with the canonical open embedding $Xto
widehat{X}$.
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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