Year: 2026
Type: preprint
Abstract: Inspired by constructions of entire curves in Oka geometry, we construct rational curves on complex Fano manifolds analytically, by alternately deforming a holomorphic disk to reduce its area and enlarging its source. Positive Ricci curvature yields an area-decreasing deformation, while an affine-lift perturbation enlarges the source at a controlled area cost. The two operations change the area and the weighted derivative by amounts we estimate explicitly, and analytic compactness passes from the resulting disks to a holomorphic sphere. The main result produces a sphere that meets a prescribed compact fiber without being contained in it, with an explicit area bound.
Source: arXiv (Cornell University)
Authors: Du, Yun-Heng, Guo, Bin, Xie, Song-Yan
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212314165