Abstract:This is a survey of recent works on the germ-equivalence problem of minimal rational curves on uniruled projective manifolds. Our main interest is when the associated varieties of minimal rational tangents form an isotrivial family of projective varieties. In this case, there is a natural G-structure on a Zariski-open subset of the underlying uniruled projective manifold, which leads to an interaction of algebraic geometry of minimal rational curves with differential geometry of geometric structures. We also discuss the related question of the formal principle for the germ-equivalence of minimal rational curves.
| Comments: | to appear in the proceedings of the 2025 SRI in Algebraic Geometry |
| Subjects: | Algebraic Geometry (math.AG); Differential Geometry (math.DG) |
| MSC classes: | 14M17, 14B20, 32C22, 14J45, 53C10 |
| Cite as: | arXiv:2605.24303 [math.AG] |
| (or arXiv:2605.24303v1 [math.AG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.24303 arXiv-issued DOI via DataCite (pending registration) |
From: Jun-Muk Hwang [view email]
[v1]
Sat, 23 May 2026 00:30:41 UTC (24 KB)
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