English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The prolongation g^{(k)} of a linear Lie algebra g \subset gl(V) 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 gl(V) 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 Sec(S) \neq P(V), theblow-up of P(V) along S has the target rigidity property, i.e., any deformationof a surjective morphism Y \to Bl_S(PV) comes from the automorphisms ofBl_S(PV).

Classification of non-degenerate projective varieties with non-zero prolongation and application to target rigidity