Special Lagrangian cycles and Calabi-Yau transitions

DOI10.1007/s00220-023-04655-3zbMath1518.53065arXiv2111.10355MaRDI QIDQ6160268

Tristan C. Collins, Sebastien Picard, Shing Tung Yau, Sergei Gukov

Publication date: 23 June 2023

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2111.10355

zbMATH Keywords

Calabi-Yau threefoldsIwasawa manifoldFu-Li-Yau geometrynon-Kähler geometries

Mathematics Subject Classification ID

Symplectic and contact topology in high or arbitrary dimension (57R17) Calabi-Yau manifolds (algebro-geometric aspects) (14J32) Calabi-Yau theory (complex-analytic aspects) (32Q25) String and superstring theories; other extended objects (e.g., branes) in quantum field theory (81T30) Symplectic field theory; contact homology (53D42) Dimensional compactification in quantum field theory (81T33) Holomorphic symplectic varieties, hyper-Kähler varieties (14J42)

Cites Work

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• Holomorphic bundles and the moduli space of \(N=1\) supersymmetric heterotic compactifications
• A construction of non-Kähler Calabi-Yau manifolds and new solutions to the Strominger system
• Continuity of extremal transitions and flops for Calabi-Yau manifolds
• Balanced metrics on non-Kähler Calabi-Yau threefolds
• Generalized Kähler geometry and the pluriclosed flow
• Solutions of the Strominger system via stable bundles on Calabi-Yau threefolds
• Non-Kähler SYZ mirror symmetry
• Calabi-Yau manifolds and SU(3) structure
• Calabi-Yau manifolds with isolated conical singularities
• On the existence of special metrics in complex geometry
• Geometric model for complex non-Kähler manifolds with \(\operatorname{SU}(3)\) structure
• Non-Kaehler heterotic string compactifications with non-zero fluxes and constant dilaton
• Anomaly cancellation and smooth non-Kähler solutions in heterotic string theory
• Torsional heterotic geometries
• Calibrated geometries
• The moduli space of 3-folds with \(K=0\) may nevertheless be irreducible
• Deformations of calibrated submanifolds
• M theory, orientifolds and \(G\)-flux.
• Calibrated fibrations
• Minimizing area among Lagrangian surfaces: the mapping problem.
• Towards \(A+B\) theory in conifold transitions for Calabi-Yau threefolds
• Finite deformations from a heterotic superpotential: holomorphic Chern-Simons and an \(L_{\infty}\) algebra
• The heterotic superpotential and moduli
• The abelian heterotic conifold
• The anomaly flow and the Fu-Yau equation
• Gauduchon metrics with prescribed volume form
• Geometric flows and Strominger systems
• Regularizing a singular special Lagrangian variety
• Symplectic conifold transitions.
• Anomaly flows
• Double solids
• Calabi-Yau manifolds and related geometries. Lectures at a summer school in Nordfjordeid, Norway, June 2001
• Special Lagrangian submanifolds with isolated conical singularities. III: Desingularization, the unobstructed case
• Massless black holes and conifolds in string theory
• Black hole condensation and the unification of string vacua
• Fivebranes, membranes and non-perturbative string theory
• Mirror symmetry is \(T\)-duality
• Existence of Hermitian-Yang-Mills metrics under conifold transitions
• Special Lagrangian submanifolds of log Calabi-Yau manifolds
• Geometric flows for the type IIA string
• Estimates for a geometric flow for the type IIB string
• Strominger-Yau-Zaslow conjecture for Calabi-Yau hypersurfaces in the Fermat family
• A construction of infinitely many solutions to the Strominger system
• Solutions to the Hull-Strominger system with torus symmetry
• On a conjecture of Candelas and de la Ossa
• The \(\partial\overline{\partial}\)-lemma for general Clemens manifolds
• A gluing construction of collapsing Calabi-Yau metrics on \(K3\) fibred 3-folds
• Invariant solutions to the Strominger system on complex Lie groups and their quotients
• Invariant solutions to the Strominger system and the heterotic equations of motion
• Infinitesimal moduli for the Strominger system and Killing spinors in generalized geometry
• A metric for heterotic moduli
• The theory of superstring with flux on non-Kähler manifolds and the complex Monge-Ampère equation
• Calibrated subbundles in noncompact manifolds of special holonomy
• The existence of supersymmetric string theory with torsion
• Embedded special Lagrangian submanifolds in Calabi-Yau manifolds
• Geometric transitions
• On the versal deformation of a complex space with an isolated singularity
• Deformations of generalized calibrations and compact non-Kähler manifolds with vanishing first Chern class
• A class of compact, complex manifolds which are not algebraic
• Calabi-Yau manifolds with torsion and geometric flows
• Heterotic quantum cohomology
• Non-K\"ahler Calabi-Yau manifolds
• GEOMETRY OF HERMITIAN MANIFOLDS
• Interior estimates for elliptic systems of partial differential equations
• DESINGULARIZATIONS OF CALABI-YAU 3-FOLDS WITH CONICAL SINGULARITIES. II. THE OBSTRUCTED CASE
• On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I
• The moduli space of special Lagrangian submanifolds
• Collapsing of Calabi-Yau manifolds and special lagrangian submanifolds
• Deformations of nodal Kähler-Einstein Del Pezzo surfaces with discrete automorphism groups
• Second Order Elliptic Systems of Differential Equations
• CFT's from Calabi-Yau four-folds
• Regularity of Hamiltonian stationary equations in symplectic manifolds
• Canonical metrics on holomorphic Courant algebroids