PreprintarXiv licencearXiv
A proof of GW/DT4 conjecture on local projective plane
Abstract
We prove a closed formula for DT4 invariants of one dimensional stable sheaves on the total space of 𝒪ℙ2(−1,−2) for all degree curve classes. During the proof, orientations of moduli spaces are chosen in a canonical way. Combining with Gopakumar-Vafa type invariants proposed and computed by Klemm-Pandharipande, we verify a conjecture proposed by the author, Maulik and Toda.
Related
- On Free and Nearly Free Conjecture of Rational Unibranched Projective Plane Curves
- A very short unified proof of Dar's conjecture and Log-Brunn--Minkowski in the plane
- Proof of the local version of the Pólya--Szegö conjecture for the torsional rigidity of polygons
- The Projective Reed-Muller Code from Quartic Curves in the Projective Plane
- On lens spaces which may embed in the complex projective plane
BibTeX
@misc{cao2026proof,
title = {{A proof of GW/DT4 conjecture on local projective plane}},
author = {Yalong Cao},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06024},
eprint = {2610.06024},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06024},
}
RIS
TY - UNPB
TI - A proof of GW/DT4 conjecture on local projective plane
AU - Yalong Cao
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.06024
UR - https://arxiv.org/abs/2610.06024
AB - We prove a closed formula for DT4 invariants of one dimensional stable sheaves on the total space of 𝒪_ℙ^2(−1,−2) for all degree curve classes. During the proof, orientations of moduli spaces are chosen in a canonical way. Combining with Gopakumar-Vafa type invariants proposed and computed by Klemm-Pandharipande, we verify a conjecture proposed by the author, Maulik and Toda.
ER -