Logarithmic Hochschild homology is functorial for strong log Fourier-Mukai transforms on smooth proper log pairs, yielding a dg bicategory of logarithmic correspondences with compatible Chern characters and Euler pairings.
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The equivariant orbifold birational classification of toroidal compactifications of tori and semiabelian schemes reduces to finding minimal compactifications in logarithmic geometry, solved combinatorially for algebraic tori, nodal curve Jacobians, and abelian-generic semiabelian schemes.
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Functoriality of logarithmic Hochschild homology of log smooth pairs
Logarithmic Hochschild homology is functorial for strong log Fourier-Mukai transforms on smooth proper log pairs, yielding a dg bicategory of logarithmic correspondences with compatible Chern characters and Euler pairings.
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Birational Classification of Orbifold Compactified Jacobians
The equivariant orbifold birational classification of toroidal compactifications of tori and semiabelian schemes reduces to finding minimal compactifications in logarithmic geometry, solved combinatorially for algebraic tori, nodal curve Jacobians, and abelian-generic semiabelian schemes.