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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Algebraic conditions identify special Lagrangian distributions in non-Kähler Calabi-Yau manifolds; explicit examples on Iwasawa and Nakamura manifolds yield non-diffeomorphic semi-flat SYZ mirror pairs.
For the standard representation of Sp_{2n}(C), the Gaiotto locus is the Bialynicki-Birula closure associated to U(Sp_{2n-2}(C)) inside the nilpotent cone, and its intersection with the stable cotangent chart is the closure of the conormal bundle to the one-spinor stratum of the generalized theta-div
Surveys Calabi-Yau literature and symmetries, characterizes isometries, introduces volume ratio formula on CICYs, and proposes symmetry-aware GNN model for Ricci-flat metrics.
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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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Non-K\"ahler Special Lagrangian submanifolds and SYZ mirror symmetry
Algebraic conditions identify special Lagrangian distributions in non-Kähler Calabi-Yau manifolds; explicit examples on Iwasawa and Nakamura manifolds yield non-diffeomorphic semi-flat SYZ mirror pairs.
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Gaiotto Loci and the Nilpotent Cone for $\mathrm{Sp}_{2n}(\mathbb C)$
For the standard representation of Sp_{2n}(C), the Gaiotto locus is the Bialynicki-Birula closure associated to U(Sp_{2n-2}(C)) inside the nilpotent cone, and its intersection with the stable cotangent chart is the closure of the conormal bundle to the one-spinor stratum of the generalized theta-div
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The Sharp Edges of Calabi-Yau Manifolds: Designing Symmetric Models for Ricci-flat Metrics
Surveys Calabi-Yau literature and symmetries, characterizes isometries, introduces volume ratio formula on CICYs, and proposes symmetry-aware GNN model for Ricci-flat metrics.