Weighted projective spaces admitting ℚ-Gorenstein smoothings to ℙ³

@misc{chen2026weighted,
  title = {{Weighted projective spaces admitting $\mathbb Q$-Gorenstein smoothings to $\mathbb P^3$}},
  author = {Jungkai Alfred Chen and Yongnam Lee},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.37242},
  eprint = {2609.37242},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.37242},
}

TY  - UNPB
TI  - Weighted projective spaces admitting ℚ-Gorenstein smoothings to ℙ^3
AU  - Jungkai Alfred Chen
AU  - Yongnam Lee
PY  - 2026
DA  - 2026/09/29
PB  - arXiv
DO  - 10.48550/arxiv.2609.37242
UR  - https://arxiv.org/abs/2609.37242
AB  - We study well-formed weighted projective threefolds that admit ℚ-Gorenstein smoothings to ℙ^3. Two families are known: the ℙ^2-type and the Q-type, and it is conjectured that these are the only possibilities. We derive numerical and local necessary conditions for such a smoothing. In addition to the anticanonical volume equation, constancy of the anticanonical Hilbert polynomial yields a further identity when all codimension two singularities are of A-type. We also obtain a semigroup condition governing the existence of global smoothing directions along codimension two curves with transverse A-type singularities. We apply these conditions to prove the expected classification in several cases. In particular, for every fixed square-free integer d, there are only finitely many ℚ-Gorenstein smoothable spaces ℙ(1,a,b,c) such that gcd(a,b)=d. Our method reduces the possible weights to a finite exact computation; for every prime p≤100, the computation produces only members of the two expected families. Finally, we prove the classification when gcd(a,b)=d and a=d^2.
ER  -