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Pseudo-Einstein Structures on Links of Isolated Singularities

  • Yoshinori Gongyo
  • Kengo Hirachi
  • Shuya Matsumoto
  • Yuya Takeuchi
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Abstract

We study Jack Lee's conjecture that, for a compact strictly pseudoconvex CR manifold M, the condition c1(T1,0M)=0 in H2(M,ℝ) implies the existence of a pseudo-Einstein structure. For links of isolated singularities, we construct counterexamples in every odd dimension at least three, with c1(T1,0M)=0 in H2(M,ℤ) and b1(M)=0. For isolated algebraic singularities of log canonical type and complex dimension at least three, we prove that the real Chern class condition is equivalent to ℚ-Cartierness of the canonical divisor, log canonicity, and the existence of a pseudo-Einstein structure. Finally, we construct a Du Bois threefold singularity whose link satisfies the real Chern class condition but admits no pseudo-Einstein structure. The initial versions of the proofs were generated with AI assistance and were subsequently revised and verified by the authors.

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Cite

BibTeXRIS
BibTeX
@misc{gongyo2026pseudoeinstein,
  title = {{Pseudo-Einstein Structures on Links of Isolated Singularities}},
  author = {Yoshinori Gongyo and Kengo Hirachi and Shuya Matsumoto and Yuya Takeuchi},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.04851},
  eprint = {2611.04851},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.04851},
}
RIS
TY  - UNPB
TI  - Pseudo-Einstein Structures on Links of Isolated Singularities
AU  - Yoshinori Gongyo
AU  - Kengo Hirachi
AU  - Shuya Matsumoto
AU  - Yuya Takeuchi
PY  - 2026
DA  - 2026/11/03
PB  - arXiv
DO  - 10.48550/arxiv.2611.04851
UR  - https://arxiv.org/abs/2611.04851
AB  - We study Jack Lee's conjecture that, for a compact strictly pseudoconvex CR manifold M, the condition c_1(T^1,0M)=0 in H^2(M,ℝ) implies the existence of a pseudo-Einstein structure. For links of isolated singularities, we construct counterexamples in every odd dimension at least three, with c_1(T^1,0M)=0 in H^2(M,ℤ) and b_1(M)=0. For isolated algebraic singularities of log canonical type and complex dimension at least three, we prove that the real Chern class condition is equivalent to ℚ-Cartierness of the canonical divisor, log canonicity, and the existence of a pseudo-Einstein structure. Finally, we construct a Du Bois threefold singularity whose link satisfies the real Chern class condition but admits no pseudo-Einstein structure. The initial versions of the proofs were generated with AI assistance and were subsequently revised and verified by the authors.
ER  -