弓形variety无限处渐近几何
摘要
我们采用梅尔罗斯(Melrose)所发展的用于研究Nakajima度量在C^2上Reduced Hilbert scheme points几何 at infinity的方法，展示了当其定义参数满足适当的genericity假设时，Nakajima度量 on quiver variety是准渐近锥形(QAC)的。因此，它具有有界几何性并具有最大体积增长。作为使用科特基(Kottke)和第二作者work to compute其Reduced L^2-cohomology并证明瓦法-威坦 conjecture的两个主要材料之一，QAC性质。另一个是针对exact wedge 3-Sasakian度量的L^2-cohomology中的消失定理，这是对加里基(Galicki)和萨拉蒙(Salamon)对于封闭3-Sasakian流形的result的推广。
引用
@article{arxiv.2410.15424,
title = {Asymptotic geometry at infinity of quiver varieties},
author = {Panagiotis Dimakis and Frédéric Rochon},
journal= {arXiv preprint arXiv:2410.15424},
year = {2025}
}
备注
31 pages, there was a problem with our proof of a spectral gap for the Hodge-deRham operator for exact wedge 3-Sasakian metrics (it was only working for forms of pure bidegree). In this new version, we provide instead a proof of our vanishing theorem in $L^2$-cohomology for exact wedge 3-Sasakian using completely different methods. We also corrected a small mistake in the proof of Theorem 4.6