2011.11239
AMPLIFIED ENDOMORPHISMS OF FANO FOURFOLDS
Jia Jia, Guolei Zhong
correctmedium confidence
- Category
- Not specified
- Journal tier
- Strong Field
- Processed
- Sep 28, 2025, 12:55 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The uploaded paper’s Theorem 1.4 proves exactly the three-way equivalence for smooth Fano fourfolds with a conic bundle and notes rationality as a consequence. The candidate solution reproduces the easy implications (toric ⇒ polarized ⇒ int-amplified) by standard toric facts and reduces the hard implication (int-amplified ⇒ toric) to the paper’s main theorem. Hence both are correct and aligned; the model’s (3) ⇒ (1) is not independent but explicitly appeals to the same result proved in the paper.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} strong field
\textbf{Justification:}
The paper provides a careful and technically advanced resolution of a key case in the characterization of varieties admitting expanding endomorphisms. The arguments are well-structured, relying on an equivariant MMP and refined structure results for conic bundles. Minor additions (explicit references for standard toric facts and a schematic overview of the reductions) would improve readability, but the core mathematics appears sound and significant.