Explicit Ricci-flat metrics on a special Schoen threefold

@misc{fu2026explicit,
  title = {{Explicit Ricci-flat metrics on a special Schoen threefold}},
  author = {Jixiang Fu and Jiuhe Liu and Yunyang Xiao and Shing-Tung Yau},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.21932},
  eprint = {2610.21932},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.21932},
}

TY  - UNPB
TI  - Explicit Ricci-flat metrics on a special Schoen threefold
AU  - Jixiang Fu
AU  - Jiuhe Liu
AU  - Yunyang Xiao
AU  - Shing-Tung Yau
PY  - 2026
DA  - 2026/10/15
PB  - arXiv
DO  - 10.48550/arxiv.2610.21932
UR  - https://arxiv.org/abs/2610.21932
AB  - We give an explicit convergent representation of the Ricci-flat Kähler metric in a one-parameter family of classes on a fixed special Schoen threefold. The threefold resolves a shifted square-torus quotient with sixteen disjoint elliptic singular curves. Radial Eguchi--Hanson product metrics and fixed flat collars define a positive background with an exact a^4 volume defect. Spherical harmonics, tangential Fourier modes, Frobenius recurrences, radial ordered integrals, and the flat quotient heat kernel specify the inverse of the background scalar linearized operator. A boundary transmission series has contraction factor 1/15. Independent weighted zeroth-order and six-dimensional Schauder estimates give the inverse bound needed for the quadratic and cubic Monge--Ampère terms. The resulting source-degree recursion converges for 0<a≤2^−2260, with explicit coefficient, potential-tail, and relative metric-tail bounds. The representation uses specified kernels, prescribed integrals, and convergent series; its parameter interval is a sufficient quantitative bound on this fixed model.
ER  -