The perfect cone compactification is a toroidal compactification which can be defined for locally symmetric varieties. We show that the perfect cone compactification of quotients of type IV domains by the action of the stable orthogonal group has canonical singularities. In particular we get that the perfect cone compactification of the moduli space of polarised K3 surfaces with ADE singularities has canonical singularities.2010 Mathematics Subject Classification. 14J10.
We extend classical results of Perego and Rapagnetta on moduli spaces of sheaves of type OG10 to moduli spaces of Bridgeland semistable objects on the Kuznetsov component of a cubic fourfold. In particular, we determine the period of this class of varieties and use it to understand when they become birational to moduli spaces of sheaves on a K3 surface.
We prove that any symplectic automorphism of finite order of an irreducible holomorphic symplectic manifold of O'Grady's 10-dimensional deformation type is trivial.
The perfect cone compactification is a toroidal compactification which can be defined for locally symmetric varieties. Let $$\overline{D_{L}/\widetilde{O}^{+}(L)}^{p}$$ D L / O ~ + ( L ) ¯ p be the perfect cone compactification of the quotient of the type IV domain $$D_{L}$$ D L associated to an even lattice L. In our main theorem we show that the pair $${ (\overline{D_{L}/\widetilde{O}^{+}(L)}^{p}, \Delta /2) }$$ ( D L / O ~ + ( L ) ¯ p , Δ / 2 ) has klt singularities, where $$\Delta $$ Δ is the closure of the branch divisor of $${ D_{L}/\widetilde{O}^{+}(L) }$$ D L / O ~ + ( L ) . In particular this applies to the perfect cone compactification of the moduli space of 2d-polarised K3 surfaces with ADE singularities when d is square-free.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.