A higher-dimensional Kummer construction associates K3^[3]-type hyper-Kähler sixfolds to Kum^3-type sixfolds, with applications to motives, derived categories, and algebraic cycle conjectures.
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The authors define integrable observables for cohomological field theories that retain integrability, recover Dubrovin-Zhang and double ramification hierarchies, introduce a new Π-class example, prove Miura equivalences among the resulting hierarchies, and supply a short new proof of Witten's 2D-grr
Any order over a reduced separated finite type scheme over a char 0 field can be resolved by an Azumaya algebra over a smooth DM stack via a sequence of stacky blow-ups.
The nth Amitsur group is a stable G-birational invariant of smooth projective G-varieties over char-0 fields for all n≥2.
Generalizes positivity theorems of Popa-Wu and Popa-Schnell for Hodge modules and Higgs bundles to smooth proper DM stacks admitting projective coarse moduli spaces.
citing papers explorer
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The hyper-Kummer construction
A higher-dimensional Kummer construction associates K3^[3]-type hyper-Kähler sixfolds to Kum^3-type sixfolds, with applications to motives, derived categories, and algebraic cycle conjectures.
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Beyond descendants: integrable observables for cohomological field theories
The authors define integrable observables for cohomological field theories that retain integrability, recover Dubrovin-Zhang and double ramification hierarchies, introduce a new Π-class example, prove Miura equivalences among the resulting hierarchies, and supply a short new proof of Witten's 2D-grr
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The Azumification of orders
Any order over a reduced separated finite type scheme over a char 0 field can be resolved by an Azumaya algebra over a smooth DM stack via a sequence of stacky blow-ups.
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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.
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Positivity in the context of Hodge modules and Higgs bundles on Deligne-Mumford stacks
Generalizes positivity theorems of Popa-Wu and Popa-Schnell for Hodge modules and Higgs bundles to smooth proper DM stacks admitting projective coarse moduli spaces.