Year: 2026
Type: preprint
Abstract: 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
Source: arXiv (Cornell University)
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7222610687