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arxiv: 1703.03160 · v2 · pith:BESEBCGMnew · submitted 2017-03-09 · 🧮 math.AG

Rational curves and prolongations of G-structures

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keywords manifoldrationalsubsetalgebraalgebraicarbitrarycomplexconnected
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In a joint work with N. Mok in 1997, we proved that for an irreducible representation $G \subset {\bf GL}(V),$ 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 $G \subset {\bf GL}(V)$ and a complex manifold containing an immersed rational curve, but the proposed proof had a flaw.

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