K3 surfaces with non-symplectic involution and compact irreducible G2-manifolds

DOI10.1017/S030500411100003XzbMath1228.53064arXiv0810.0957OpenAlexW3104876813MaRDI QIDQ3089115

Nam-Hoon Lee, Alexei Kovalev

Publication date: 23 August 2011

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0810.0957

Mathematics Subject Classification ID

(K3) surfaces and Enriques surfaces (14J28) Issues of holonomy in differential geometry (53C29)

Related Items (33)

Recent Results on Closed G 2-Structures ⋮ On the rational cohomology ring of a certain \(G_2\)-manifold ⋮ On gauge enhancement and singular limits in \(G_{2}\) compactifications of M-theory ⋮ The landscape of M-theory compactifications on seven-manifolds with \(G_{2}\) holonomy ⋮ Asymptotically cylindrical Calabi-Yau 3-folds from weak Fano 3-folds ⋮ A compact \(\mathrm G_2\)-calibrated manifold with first Betti number \(b_1 = 1\) ⋮ Calabi-Yau manifolds from pairs of non-compact Calabi-Yau manifolds ⋮ A construction of \(G_2\)-manifolds from K3 surfaces with a \(\mathbb{Z}_2^2\)-action ⋮ \(K3\) surfaces with non-symplectic automorphisms of order three and Calabi-Yau orbifolds ⋮ Calabi–Yau threefolds with non‐Gorenstein involutions ⋮ Closed \({G_2}\)-structures on compact quotients of Lie groups ⋮ A compact non‐formal closed G₂manifold with b1=1$b_1=1$ ⋮ Extra-twisted connected sum \(G_2\)-manifolds ⋮ Mirror pairs of Calabi-Yau threefolds from mirror pairs of quasi-Fano threefolds ⋮ Associative submanifolds in Joyce's generalised Kummer constructions ⋮ Exact \(\mathrm{G}_2\)-structures on compact quotients of Lie groups ⋮ Diffeomorphism classes of the doubling Calabi-Yau threefolds with Picard number two ⋮ K3 surfaces with two involutions and low Picard number ⋮ Constructions of Compact $$G_2$$-Holonomy Manifolds ⋮ Current Progress on $$\mathrm{{G}}_2$$-Instantons over Twisted Connected Sums ⋮ Tops as building blocks for \(G_2\) manifolds ⋮ \(G_2\)-manifolds from \(K3\) surfaces with non-symplectic automorphisms ⋮ Generalised Kummer construction and the cohomology rings of $G_2$-manifolds ⋮ Hermitian Yang–Mills metrics on reflexive sheaves over asymptotically cylindrical Kähler manifolds ⋮ Corrigendum to ``\(G_2\)-manifolds from \(K3\) surfaces with non-symplectic automorphisms ⋮ A new construction of compact torsion-free \(G_2\)-manifolds by gluing families of Eguchi-Hanson spaces ⋮ Effective action from M-theory on twisted connected sum \(G_2\)-manifolds ⋮ M-theory and orientifolds ⋮ Matter from geometry without resolution ⋮ Gluing construction of compact \(\mathrm{Spin}(7)\)-manifolds ⋮ Supersymmetric protection and the swampland ⋮ \(\mathrm{G}_{2}\)-instantons over twisted connected ⋮ The moduli space of asymptotically cylindrical Calabi-Yau manifolds

Cites Work

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• Asymptotically cylindrical 7-manifolds of holonomy \(G_{2}\) with applications to compact irreducible \(G _{2}\)-manifolds
• Classification of Fano 3-folds with \(B_ 2 \geq 2\)
• Factoring polynomials with rational coefficients
• Mirror symmetry for lattice polarized \(K3\) surfaces
• Factor groups of groups of automorphisms of hyperbolic forms with respect to subgroups generated by 2-reflections. Algebro-geometric applications
• Twisted connected sums and special Riemannian holonomy

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