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math.DG2026
Local Models for Special Kähler Metric Singularities Along the Discriminant Locus of the Hitchin Base
Zhenxi Huang, Shuo Wang, Bin Xu
Freed (arXiv:hep-th/9712042) formulated special Kähler structures; in particular, the regular locus of the Hitchin base carries such a st…
math.DG2025
Complex structures of the Gibbons-Hawking ansatz with infinite topological type
Wenxin He, Bin Xu
In this paper, we study the complex structures of complete hyperkähler four-manifolds of infinite topological type arising from the Gibbons-Hawking ansatz. We show that for almost…
math.DG2025
Counting Rational Curves and Standard Complex Structures on HyperKähler ALE 4-manifolds
Yuanjiu Lyu, Bin Xu
All hyperKähler ALE 4-manifolds with a given non-trivial finite group in at infinity are parameterized by an open dense subset of a real linear space of dimension …