A canonical degeneration of generalized Kummer varieties is obtained by closing the relative Kum inside the compactified relative Hilbert scheme of a degenerating abelian surface family, with the dual complex for n=2 being PL-homeomorphic to the 2-simplex.
From logarithmic Hilbert schemes to degenerations of hyperk\” ahler varieties
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The authors introduce logarithmic coherent sheaves in the logarithmic étale topology and tools to reduce homological algebra computations to alterations, unifying logarithmic Quot spaces, Picard groups, and parabolic sheaves.
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Degenerations of generalized Kummer varieties
A canonical degeneration of generalized Kummer varieties is obtained by closing the relative Kum inside the compactified relative Hilbert scheme of a degenerating abelian surface family, with the dual complex for n=2 being PL-homeomorphic to the 2-simplex.
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Coherent sheaves in logarithmic geometry
The authors introduce logarithmic coherent sheaves in the logarithmic étale topology and tools to reduce homological algebra computations to alterations, unifying logarithmic Quot spaces, Picard groups, and parabolic sheaves.