
Journal of Lie Theory 31 (2021), No. 1, 127148 Copyright Heldermann Verlag 2021 The Regularity of AlmostCommuting Partial GrothendieckSpringer Resolutions and Parabolic Analogs of CalogeroMoser Varieties Mee Seong Im Dept. of Mathematical Sciences, United States Military Academy, West Point, NY 10996, U.S.A. im@usna.edu Travis Scrimshaw School of Mathematics and Physics, University of Queensland, St. Lucia, QLD 4072, Australia t.scrimshaw@uq.edu.au [Abstractpdf] Consider the moment map $\mu \colon T^*(\mathfrak{p} \times \mathbb{C}^n) \to \mathfrak{p}^*$ for a parabolic subalgebra $\mathfrak{p}$ of $\mathfrak{gl}_n(\mathbb{C})$. We prove that the preimage of $0$ under $\mu$ is a complete intersection when $\mathfrak{p}$ has finitely many $P$orbits, where $P\subseteq \operatorname{GL}_n(\mathbb{C})$ is a parabolic subgroup such that $\operatorname{Lie}(P) = \mathfrak{p}$, and give an explicit description of the irreducible components. This allows us to study nearby fibers of $\mu$ as they are equidimensional, and one may also construct GIT quotients $\mu^{1}(0) /\!\!/_{\chi} P$ by varying the stability condition $\chi$. Finally, we study a variety analogous to the scheme studied by Wilson with connections to a CalogeroMoser phase space where only some of particles interact. Keywords: GrothendieckSpringer resolution, moment map, complete intersection. MSC: 14M10, 53D20, 17B08, 14L30; 14L24, 20G20. [ Fulltextpdf (214 KB)] for subscribers only. 