Classification of non-degenerate projective varieties with non-zero prolongation and application to target rigidity - Mathematics > Algebraic GeometryReportar como inadecuado




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Abstract: The prolongation g^{k} of a linear Lie algebra g \subset glV plays animportant role in the study of symmetries of G-structures. Cartan andKobayashi-Nagano have given a complete classification of irreducible linear Liealgebras g \subset glV with non-zero prolongations.If g is the Lie algebra aut\hat{S} of infinitesimal linear automorphisms ofa projective variety S \subset \BP V, its prolongation g^{k} is related tothe symmetries of cone structures, an important example of which is the varietyof minimal rational tangents in the study of uniruled projective manifolds.From this perspective, understanding the prolongation aut\hat{S}^{k} isuseful in questions related to the automorphism groups of uniruled projectivemanifolds. Our main result is a complete classification of irreduciblenon-degenerate nonsingular variety with non zero prolongations, which can beviewed as a generalization of the result of Cartan and Kobayashi-Nagano. As anapplication, we show that when $S$ is linearly normal and SecS eq PV, theblow-up of PV along S has the target rigidity property, i.e., any deformationof a surjective morphism Y \to Bl SPV comes from the automorphisms ofBl SPV.



Autor: Baohua Fu, Jun-Muk Hwang

Fuente: https://arxiv.org/







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