Pith. Sign in

RECORD

On decompositions for Fano schemes of intersections of two quadrics

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
Pieter Belmans, Jishnu Bose, Sarah Frei, Benjamin Gould, James Hotchkiss, Alicia Lamarche, Jack Petok, Cristian Rodriguez Avila
show 1 more author
Saket Shah

Algebraic Geometry · Submitted 19 Mar 2024

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

The authors' main claim We propose conjectural semiorthogonal decompositions for Fano schemes of linear subspaces on intersections of two quadrics, in terms of symmetric powers of the associated hyperelliptic (resp. stacky) curve.

how it is stated · speculative 0.99 read the record →

Comment (0) Read on arXiv ↗
Cite ▾
arXiv ID2403.12517 (version 2)
Pith IDOIWSQVSV, Pith's permanent record of this paper and its review
CitationAlicia Lamarche, Benjamin Gould, Cristian Rodriguez Avila, Jack Petok, James Hotchkiss, Jishnu Bose, Pieter Belmans, Saket Shah, Sarah Frei. "On decompositions for Fano schemes of intersections of two quadrics." arXiv:2403.12517 (2024). https://pith.science/paper/OIWSQVSV
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, 3,698 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.69 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.20 · compares with prior results 0.67 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We propose conjectural semiorthogonal decompositions for Fano schemes of linear subspaces on intersections of two quadrics, in terms of symmetric powers of the associated hyperelliptic (resp. stacky) curve. When the intersection is odd-dimensional, we moreover conjecture an identity in the Grothendieck ring of varieties and other motivic contexts. The evidence for these conjectures is given by upgrading recent results of Chen-Vilonen-Xue, to obtain formulae for the Hodge numbers of these Fano schemes. This allows us to numerically verify the conjecture in the hyperelliptic case, and establish a combinatorial identity as evidence for the stacky case.

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 propose conjectural semiorthogonal decompositions for Fano schemes of linear subspaces on intersections of two quadrics, in terms of symmetric powers of the associated hyperelliptic (resp. stacky) curve. contribution 0.98 0.78 0.67 speculative 0.99
s1 When the intersection is odd-dimensional, we moreover conjecture an identity in the Grothendieck ring of varieties and other motivic contexts. contribution 0.91 0.37 0.11 speculative 1.00
s2 The evidence for these conjectures is given by upgrading recent results of Chen-Vilonen-Xue, to obtain formulae for the Hodge numbers of these Fano schemes. method 0.75 0.86 0.07 asserted 0.99
s3 This allows us to numerically verify the conjecture in the hyperelliptic case, and establish a combinatorial identity as evidence for the stacky case. result 0.86 0.92 0.12 asserted 0.97

What kind of paper the classifier reports this is: theoretical result 0.54 · evidence from simulation or computation 0.59.

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 propose conjectural semiorthogonal decompositions for Fano schemes of linear subspaces on intersections of two quadrics, in terms of symmetric powers of the associated hyperelliptic (resp. stacky) curve. When the intersection is odd-dimensional, we moreover conjecture an identity in the Grothendieck ring of varieties and other motivic contexts. The evidence for these conjectures is given by upgrading recent results of Chen-Vilonen-Xue, to obtain formulae for the Hodge numbers of these Fano schemes. This allows us to numerically verify the conjecture in the hyperelliptic case, and establish a combinatorial identity as evidence for the stacky case.

Human review

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

How the literature uses it

1 arXiv paper cite this in 1 sentence

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

Papers citing it

Cites it as background 1 paper
  • There is a large body of conjectures on explicit semiorthogonal decompositions of Fano varieties, which are often obtained by analyzing Hodge diamonds and using the additivity of Hochschild homology in semiorthogonal decompositions [ref] *Theorem 1.5; see [ref] for a recent example related to our paper.These predictions are not easy to turn into proofs.

    Noncommutative resolution of $SU_C(2)$ · Introduction · 0.91

Discussion

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