超环面簇、$W$-Hilbert概形与Coulomb分支
代数几何
2026-04-24 v6 高能物理 - 理论
微分几何
辛几何
摘要
我们研究配备Weyl群辛作用的仿射超环面簇的横向等变Hilbert概形。特别地,我们证明Braverman、Finkelberg与Nakajima的Coulomb分支可由此类Hilbert概形或其Hamilton约化得到。此外我们提出,非余切型表示的Coulomb分支亦以此方式获得。我们还研究了这些对象上假定的完备超凯勒度量。我们描述了它们的扭量空间,并且在超环面簇的辛商构造是 -等变时(包含余切型Coulomb分支),我们证明该超凯勒度量可描述为带两端极点及中部间断的区间上修正Nahm方程解模空间上的自然 -度量,其中间断由一新对象描述:典范关联于超环面簇的超球簇。
引用
@article{arxiv.2304.08125,
title = {Hypertoric varieties, $W$-Hilbert schemes, and Coulomb branches},
author = {Roger Bielawski and Lorenzo Foscolo},
journal= {arXiv preprint arXiv:2304.08125},
year = {2026}
}
备注
Please note that the proof of Proposition 6.5 and hence of Corollary 6.7 is wrong. In fact, the Theorem stated in the Introduction is false in full generality. The relation between transverse Hilbert schemes and Coulomb branches will be clarified in the forthcoming paper by Ben Webster. The authors are currently rewriting the paper (this version is unchanged from the last one)