Rational curves and prolongations of G-structures

2017/03/09 by Jun-Muk Hwang, Hwang, Jun-Muk
Mathematics · #14M17 #32Q30 #53C15 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1703.03160

openalex publication_date 2017/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In a joint work with N. Mok in 1997, we proved that for an irreducible representation G ⊂ \bf GL(V), if a holomorphic G-structure exists on a uniruled projective manifold, then the Lie algebra of G has nonzero prolongation. We tried to generalize this to an arbitrary connected algebraic subgroup G ⊂ \bf GL(V) and a complex manifold containing an immersed rational curve, but the proposed proof had a flaw.

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