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.
Existence of moduli spaces for algebraic stacks
3 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
We provide necessary and sufficient conditions for when an algebraic stack admits a good moduli space and prove a semistable reduction theorem for points of algebraic stacks equipped with a $\Theta$-stratification. These results provide a generalization of the Keel--Mori theorem to moduli problems whose objects have positive dimensional automorphism groups and give criteria on the moduli problem to have a separated or proper good moduli space. To illustrate our method, we apply these results to construct proper moduli spaces parameterizing semistable $\mathcal{G}$-bundles on curves and moduli spaces for objects in abelian categories.
representative citing papers
Any Farey triangle corresponds to a variant of the Colmez-Fontaine fundamental lemma, with the original lemma matching the triangle (1/0, 1/1, 0/1).
For K3^[n]-type hyper-Kähler manifolds with antisymplectic involution from ample class of square 2 and divisibility 2, one fixed component is Fano of index 3; the second component in the LLSvS 8-fold is of general type.
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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Modular variants of p-adic fundamental sequence
Any Farey triangle corresponds to a variant of the Colmez-Fontaine fundamental lemma, with the original lemma matching the triangle (1/0, 1/1, 0/1).
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The geometry of antisymplectic involutions, II
For K3^[n]-type hyper-Kähler manifolds with antisymplectic involution from ample class of square 2 and divisibility 2, one fixed component is Fano of index 3; the second component in the LLSvS 8-fold is of general type.