Projective Kummer-type manifolds with finite-order symplectic birational self-maps acting nontrivially on H² are twisted modular except for Picard rank 3 cases characterized by their NS lattices; specific Mukai vectors are identified for finite-order wall-crossing maps on modular examples.
Projectivity and birational geometry of
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Moduli spaces of ξ⃗-parabolic Higgs bundles realize partial compactifications of the restricted Hitchin map on symplectic leaves of meromorphic Higgs bundle moduli spaces and provide symplectic resolutions of their normalizations.
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Finite order symplectic birational self-maps on Kummer-type manifolds
Projective Kummer-type manifolds with finite-order symplectic birational self-maps acting nontrivially on H² are twisted modular except for Picard rank 3 cases characterized by their NS lattices; specific Mukai vectors are identified for finite-order wall-crossing maps on modular examples.
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Symplectic leaves of meromorphic Hitchin systems
Moduli spaces of ξ⃗-parabolic Higgs bundles realize partial compactifications of the restricted Hitchin map on symplectic leaves of meromorphic Higgs bundle moduli spaces and provide symplectic resolutions of their normalizations.