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.
The orbifold Chow ring of toric Deligne-Mumford stacks , volume=
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The nth Amitsur group is a stable G-birational invariant of smooth projective G-varieties over char-0 fields for all n≥2.
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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.
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Birational invariance of higher Amitsur groups
The nth Amitsur group is a stable G-birational invariant of smooth projective G-varieties over char-0 fields for all n≥2.