Tropical and non-Archimedean Monge-Ampère equations for a class of Calabi-Yau hypersurfaces
DOI10.1016/j.aim.2024.109494arXiv2208.13697MaRDI QIDQ6201191
Nicholas McCleerey, Enrica Mazzon, Mattias Jonsson, Jakob Hultgren
Publication date: 20 February 2024
Published in: Advances in Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2208.13697
Calabi-Yau manifoldsSYZ conjectureMonge-Ampère equationsspecial Lagrangian fibrationessential skeleton
Calabi-Yau manifolds (algebro-geometric aspects) (14J32) Calabi-Yau theory (complex-analytic aspects) (32Q25) Affine differential geometry (53A15) Mirror symmetry (algebro-geometric aspects) (14J33) Non-Archimedean analysis (32P05) Combinatorial aspects of algebraic geometry (05E14) Applications of tropical geometry (14T90)
Cites Work
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- A variational approach to complex Monge-Ampère equations
- Real Monge-Ampère equations and Kähler-Ricci solitons on toric log Fano varieties
- An extension theorem for Kähler currents with analytic singularities
- The Monge-Ampère equation and its applications
- The arithmetic Hodge index theorem for adelic line bundles
- Gromov-Hausdorff collapsing of Calabi-Yau manifolds
- Period integrals from wall structures via tropical cycles, canonical coordinates in mirror symmetry and analyticity of toric degenerations
- Growth of balls of holomorphic sections and energy at equilibrium
- Large complex structure limits of \(K3\) surfaces
- Remarques sur les variétés localement hessiennes. (Remarks on locally Hessian manifolds)
- Mirror symmetry is \(T\)-duality
- Collapsing of abelian fibered Calabi-Yau manifolds
- Solutions to the Monge-Ampère equation with polyhedral and Y-shaped singularities
- Tropical and non-Archimedean limits of degenerating families of volume forms
- Special Lagrangian submanifolds of log Calabi-Yau manifolds
- Collapsing \(K3\) surfaces, tropical geometry and moduli compactifications of Satake, Morgan-Shalen type
- Compactifying torus fibrations over integral affine manifolds with singularities
- Degenerated Calabi-Yau varieties with infinite components, moduli compactifications, and limit toroidal structures
- On the extension of quasiplurisubharmonic functions
- Strominger-Yau-Zaslow conjecture for Calabi-Yau hypersurfaces in the Fermat family
- Spaces of norms, determinant of cohomology and Fekete points in non-Archimedean geometry
- A comparison of the real and non-Archimedean Monge-Ampère operator
- An optimal transport approach to Monge-Ampère equations on compact Hessian manifolds
- Tropical varieties for non-archimedean analytic spaces
- Mirror symmetry via logarithmic degeneration data. I
- The essential skeleton of a degeneration of algebraic varieties
- Introduction to Toric Varieties. (AM-131)
- Weight functions on non-Archimedean analytic spaces and the Kontsevich–Soibelman skeleton
- Local heights of subvarieties over non-archimedean fields
- The Regularity of Mappings with a Convex Potential
- On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I
- Positive Line Bundles on Arithmetic Varieties
- Introduction
- Extension of plurisubharmonic functions with growth control
- [https://portal.mardi4nfdi.de/wiki/Publication:5126728 Differentiability of non-archimedean volumes and non-archimedean Monge�Amp�re equations\n (with an appendix by Robert Lazarsfeld)]
- Solution to a non-Archimedean Monge-Ampère equation
- Partial Regularity for Singular Solutions to the Monge‐Ampère Equation
- The non-archimedean SYZ fibration
- Arithmetic geometry of toric varieties. Metrics, measures and heights
- Mirror Symmetry and the Strominger-Yau-Zaslow conjecture
- Mesures et équidistribution sur les espaces de Berkovich
- Notions of convexity
- On the two types of affine structures for degenerating Kummer surfaces -- non-Archimedean vs Gromov-Hausdorff limits --
- Special Lagrangian Fibrations, Berkovich Retraction, and Crystallographic Groups
- Metric SYZ conjecture and non-Archimedean geometry
- Metric SYZ conjecture for certain toric Fano hypersurfaces
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