2506.02275
Discrete Painlevé equations from pencils of quadrics in P3 with branching generators
Jaume Alonso, Yuri B. Suris
correctmedium confidence
- Category
- math.DS
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper’s Theorem 1 defines L in exactly the two cases (Q∞ independent of X3 or of X1) and proves by a direct computation that L sends Qλ(ν) to Qλ(ν̂) and fixes the base curve off the stated coordinate hyperplane. The candidate solution reproduces the same computation and homogeneity argument (Q∞(L(X)) scaling by X4^2 or X2^2), reaching the same conclusions with the same structure of proof. See Theorem 1 and its proof in the paper ; see also the pencil set-up Qλ = Q0 − λQ∞ with Q0 = X1X2 − X3X4 in the general scheme .
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The theorem and computation are correct and align with the paper’s framework. Explicitly noting the homogeneity step that turns Q∞(X̂) into a scaled Q∞(X) would aid readability; otherwise, the result is sound and well-placed in the broader construction.