{"arxiv_id":"1011.0288","incoming":{"papers":2,"sentences":9,"groups":[{"kind":"contests","label":"Contests it","papers":1,"sentences":1,"quotes":[{"arxiv_id":"2109.05350","title":"Intrinsic holonomy and curved cosets of Cartan geometries","url":"/paper/2109.05350","section":"Inessential automorphism groups of parabolic geometries","sentence":"We imagine that this was the intended definition in [ref] , since all of the results from that paper seem to work otherwise verbatim with this definition, but as written it was assumed that $λ_*^$ acts by scalar multiplication on each grading component $𝔤_i$, in which case it is not hard to see that $λ_*^$ must be a scalar multiple of the grading element.","intent_p":0.97,"contests_p":0.79}]},{"kind":"comparison","label":"Compares with it","papers":1,"sentences":3,"quotes":[{"arxiv_id":"2109.05350","title":"Intrinsic holonomy and curved cosets of Cartan geometries","url":"/paper/2109.05350","section":"Inessential automorphism groups of parabolic geometries","sentence":"While Proposition [ref] does, more or less immediately, recover Theorem 1.2 from [ref] , and it does tell us that $ξ$ is $λ$-essential if $ω_ℯ^norm(ξ)∉(λ_*)$, the considerations above severely limit its ability to obtain more global results about $λ$-inessential infinitesimal automorphisms.","intent_p":0.86,"contests_p":null}]}],"unlabelled_sentences":5},"outgoing":{"papers":6,"sentences":29,"groups":[{"kind":"extends","label":"Builds on","papers":2,"sentences":4,"quotes":[{"arxiv_id":"0909.0044","title":"Local Dynamics of Conformal Vector Fields","url":"/paper/0909.0044","section":"Organization of the text and summary of main results","sentence":"Then, we apply the identity reviewed in Section [ref] to prove a generalization of results of [ref] , which give a “dictionary” relating essentiality of an infinitesimal automorphism near a singularity $x_0$ to properties of its holonomy $h^t$ at $x_0$, a one-parameter subgroup of $P$ which is determined up to conjugacy (cf. Definition [ref]; it should be emphasized that this notion of “holonomy” of the singularity of an infinitesimal automorphism is distinct from the holonomy of, e.g., a Cartan connection which is common in the literature).","intent_p":0.96,"contests_p":null},{"arxiv_id":"math.DG/0508535","title":null,"url":"/paper/math.DG/0508535","section":"Background results on infinitesimal automorphisms","sentence":"The following identity was proven for parabolic geometries in [ref] and the proof carries over without substantive changes to Cartan geometries of general type (cf. also Lemma 1.5.12 in [ref] ):","intent_p":0.8,"contests_p":null}]},{"kind":"method_or_tool","label":"Uses the method or tool of","papers":2,"sentences":3,"quotes":[{"arxiv_id":"math.DG/0608537","title":null,"url":"/paper/math.DG/0608537","section":"Lichnérowicz theorem for rank one parabolic geometries","sentence":"The assumption that the parabolic geometries are of rank one type is key for the argument in [ref] , because it allows the author to exploit the so-called “north-south dynamics” on the homogeneous model $G/P$.","intent_p":0.8,"contests_p":null},{"arxiv_id":"0909.0044","title":"Local Dynamics of Conformal Vector Fields","url":"/paper/0909.0044","section":"Acknowledgements","sentence":"I am grateful to Charles Frances for discussions about the methods used in [ref] and [ref] , and to Felipe Leitner for useful comments on an earlier version of the text.","intent_p":0.97,"contests_p":null}]},{"kind":"background","label":"Cites as background","papers":2,"sentences":4,"quotes":[{"arxiv_id":"math.DG/0001166","title":null,"url":"/paper/math.DG/0001166","section":"Background on parabolic geometries and their Weyl structures","sentence":"Let us begin by recalling the definitions of parabolic geometries and their Weyl structures (the latter, introduced by A. Čap and J. Slovák in [ref] , will be central to our notion of essential parabolic structures).","intent_p":0.97,"contests_p":null},{"arxiv_id":"math.DG/0508535","title":null,"url":"/paper/math.DG/0508535","section":"Background results on infinitesimal automorphisms","sentence":"We recall some general notions, mainly following the development of [ref] (cf. also 1.5 of [ref] ), in the setting of a general Cartan geometry $(→M,ω)$ of type $(G,P)$ (for now not assumed to be of parabolic type).","intent_p":1.0,"contests_p":null}]}],"unlabelled_sentences":18},"claims":[],"thresholds":{"intent_p":0.8,"supports_p":0.95,"contests_p":0.7},"method":"Citing sentences come from each paper's LaTeX source; every \\cite marks the sentence and the works it cites. Pith's classifier typed each sentence. A label is shown at intent probability 0.8 or more (0.95 for support), a contest at 0.7 or more. Measured accuracy against two blind model families is at https://pith.science/accuracy. The quoted sentences are the citing authors' own.","held_up":null,"_links":{"html":"https://pith.science/paper/1011.0288"}}