Pith. Sign in

RECORD

Reduction of Generalized Complex Structures

PaperPDF from arXiv

data files

Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
X Bluesky LinkedIn Reddit Hacker News
Mathieu Stienon, Ping Xu

Differential Geometry · Submitted 18 Sep 2005

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

The authors' main claim We describe a sufficient condition for the reduction to hold, which includes the Marsden-Weinstein reduction of symplectic manifolds and the reduction of the complex structures in K\"ahler manifolds as special cases.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗
Cite ▾
arXiv IDmath/0509393 (version 2)
Pith IDJYRMPS3M, Pith's permanent record of this paper and its review
CitationMathieu Stienon, Ping Xu. "Reduction of Generalized Complex Structures." arXiv:math/0509393 (2005). https://pith.science/paper/JYRMPS3M
Claim paper

The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,493 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.29 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.02 · compares with prior results 0.73 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

We study reduction of generalized complex structures. More precisely, we investigate the following question. Let $J$ be a generalized complex structure on a manifold $M$, which admits an action of a Lie group $G$ preserving $J$. Assume that $M_0$ is a $G$-invariant smooth submanifold and the $G$-action on $M_0$ is proper and free so that $M_G:=M_0/G$ is a smooth manifold. Under what condition does $J$ descend to a generalized complex structure on $M_G$? We describe a sufficient condition for the reduction to hold, which includes the Marsden-Weinstein reduction of symplectic manifolds and the reduction of the complex structures in K\"ahler manifolds as special cases. As an application, we study reduction of generalized K\"ahler manifolds.

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 We study reduction of generalized complex structures. contribution 0.94 0.88 0.04 asserted 0.72
s1 More precisely, we investigate the following question. background 0.53 0.67 0.01 unclear 0.82
s2 Let $J$ be a generalized complex structure on a manifold $M$, which admits an action of a Lie group $G$ preserving $J$. background 0.96 0.13 0.02 asserted 0.89
s3 Assume that $M_0$ is a $G$-invariant smooth submanifold and the $G$-action on $M_0$ is proper and free so that $M_G:=M_0/G$ is a smooth manifold. background 0.97 0.16 0.02 asserted 0.95
s4 Under what condition does $J$ descend to a generalized complex structure on $M_G$? background 0.56 0.07 0.03 unclear 0.99
s5 We describe a sufficient condition for the reduction to hold, which includes the Marsden-Weinstein reduction of symplectic manifolds and the reduction of the complex structures in K\"ahler manifolds as special cases. result 0.60 0.92 0.81 asserted 1.00
s6 As an application, we study reduction of generalized K\"ahler manifolds. contribution 1.00 0.91 0.07 asserted 0.95

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

What was examined, and what was not

sources read
  • arXiv listing abstract v2
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

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

We study reduction of generalized complex structures. More precisely, we investigate the following question. Let $J$ be a generalized complex structure on a manifold $M$, which admits an action of a Lie group $G$ preserving $J$. Assume that $M_0$ is a $G$-invariant smooth submanifold and the $G$-action on $M_0$ is proper and free so that $M_G:=M_0/G$ is a smooth manifold. Under what condition does $J$ descend to a generalized complex structure on $M_G$? We describe a sufficient condition for the reduction to hold, which includes the Marsden-Weinstein reduction of symplectic manifolds and the reduction of the complex structures in K\"ahler manifolds as special cases. As an application, we study reduction of generalized K\"ahler manifolds.

Human review

How Pith checks papers → · Full audit of this paper →

References

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.