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On the Szeg\"o kernel of Cartan-Hartogs domains

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Andrea Loi, Daria Uccheddu, Michela Zedda

Differential Geometry · Submitted 6 Oct 2014

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim In particular we compute the Szeg\"o kernel of the disk bundle over a Cartan-Hartogs domain based on a bounded symmetric domain.

how it is stated · asserted 1.00 read the record →

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arXiv ID1410.1508 (version 1)
Pith IDIOMP5W22, Pith's permanent record of this paper and its review
CitationAndrea Loi, Daria Uccheddu, Michela Zedda. "On the Szeg\"o kernel of Cartan-Hartogs domains." arXiv:1410.1508 (2014). https://pith.science/paper/IOMP5W22
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,674 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.09 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.34 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

Inspired by the work of Z. Lu and G. Tian [21] in the compact setting, in this paper we address the problem of studying the Szeg\"o kernel of the disk bundle over a noncompact K\"ahler manifold. In particular we compute the Szeg\"o kernel of the disk bundle over a Cartan-Hartogs domain based on a bounded symmetric domain. The main ingredients in our analysis are the fact that every Cartan-Hartogs domain can be viewed as an "iterated" disk bundle over its base and the the ideas given in [4] for the computation of the Szeg\"o kernel of the disk bundle over an Herimitian symmetric space of compact type.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Inspired by the work of Z. Lu and G. background 1.00 0.05 0.02 unclear 0.95
s1 Tian [21] in the compact setting, in this paper we address the problem of studying the Szeg\"o kernel of the disk bundle over a noncompact K\"ahler manifold. contribution 0.67 0.36 0.07 asserted 0.94
s2 In particular we compute the Szeg\"o kernel of the disk bundle over a Cartan-Hartogs domain based on a bounded symmetric domain. contribution 0.53 0.95 0.66 asserted 1.00
s3 The main ingredients in our analysis are the fact that every Cartan-Hartogs domain can be viewed as an "iterated" disk bundle over its base and the the ideas given in [4] for the computation of the Szeg\"o kernel of the disk bundle over an Herimitian symmetric space of compact type. method 0.98 0.29 0.10 asserted 0.99

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.99.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

Inspired by the work of Z. Lu and G. Tian [21] in the compact setting, in this paper we address the problem of studying the Szeg\"o kernel of the disk bundle over a noncompact K\"ahler manifold. In particular we compute the Szeg\"o kernel of the disk bundle over a Cartan-Hartogs domain based on a bounded symmetric domain. The main ingredients in our analysis are the fact that every Cartan-Hartogs domain can be viewed as an "iterated" disk bundle over its base and the the ideas given in [4] for the computation of the Szeg\"o kernel of the disk bundle over an Herimitian symmetric space of compact type.

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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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