Pith. Sign in

RECORD

The asymptotic growth of equivariant sections of positive and big line bundles

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
Roberto Paoletti

Algebraic Geometry · Submitted 16 Jul 2002

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

The authors' main claim We consider the asymptotic growth of these summands, under various positivity conditions on L.

how it is stated · asserted 0.53 read the record →

Comment (0) Read on arXiv ↗
Cite ▾
arXiv IDmath/0207128 (version 1)
Pith IDAHWOPHS4, Pith's permanent record of this paper and its review
CitationRoberto Paoletti. "The asymptotic growth of equivariant sections of positive and big line bundles." arXiv:math/0207128 (2002). https://pith.science/paper/AHWOPHS4
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, 2,966 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.11 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.05 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

If a finite group acts holomorphically on a pair (X,L), where X is a complex projective manifold and L a line bundle on it, for every k the space of holomorphic global section of the k-th power of L splits equivariantly according to the irreducible representations of G. We consider the asymptotic growth of these summands, under various positivity conditions on L. The methods apply also to the context of almost complex quantization.

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 If a finite group acts holomorphically on a pair (X,L), where X is a complex projective manifold and L a line bundle on it, for every k the space of holomorphic global section of the k-th power of L splits equivariantly according to the irreducible representations of G. background 0.99 0.10 0.07 asserted 1.00
s1 We consider the asymptotic growth of these summands, under various positivity conditions on L. contribution 0.99 0.82 0.10 asserted 0.53
s2 The methods apply also to the context of almost complex quantization. contribution 0.43 0.49 0.05 asserted 0.94

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 v1
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

If a finite group acts holomorphically on a pair (X,L), where X is a complex projective manifold and L a line bundle on it, for every k the space of holomorphic global section of the k-th power of L splits equivariantly according to the irreducible representations of G. We consider the asymptotic growth of these summands, under various positivity conditions on L. The methods apply also to the context of almost complex quantization.

Human review

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

Discussion

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