Skeleta of affine hypersurfaces

DOI10.2140/gt.2014.18.1343zbMath1326.14102arXiv1211.5263OpenAlexW2128011898MaRDI QIDQ2509852

Helge Ruddat, Nicolò Sibilla, David Treumann, Eric Zaslow

Publication date: 31 July 2014

Published in: Geometry \& Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1211.5263

zbMATH Keywords

triangulationNewton polytopehypersurfaceretractionlog geometryaffinehomotopy equivalenceskeletontoric degenerationKato-Nakayama space

Mathematics Subject Classification ID

Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Hypersurfaces and algebraic geometry (14J70) Affine geometry (14R99)

Related Items

Lagrangian skeleta and plane curve singularities, An Introduction to Hodge Structures, Tailoring a pair of pants, Kato-Nakayama spaces, infinite root stacks and the profinite homotopy type of log schemes, Legendrian weaves: \(N\)-graph calculus, flag moduli and applications, Mirror symmetry for the Landau-Ginzburg \(A\)-model \(M=\mathbb{C}^n\), \(W= z_1 \cdots z_n\), Real loci in (log) Calabi-Yau manifolds via Kato-Nakayama spaces of toric degenerations, Lagrangian skeleta of hypersurfaces in \((\mathbb{C}^*)^n\), Topological Fukaya category and mirror symmetry for punctured surfaces, Perverse curves and mirror symmetry, Constructing local models for Lagrangian torus fibrations, Kasteleyn operators from mirror symmetry

Cites Work

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• Lagrangian fibrations on blowups of toric varieties and mirror symmetry for hypersurfaces
• Ribbon graphs and mirror symmetry
• Towards mirror symmetry for varieties of general type
• Relative rounding in toric and logarithmic geometry
• A categorification of Morelli's theorem
• From real affine geometry to complex geometry
• The fundamental category of a stratified space
• Variations of the mixed Hodge structure of affine hypersurfaces in algebraic tori
• Log smooth deformation theory
• log Betti cohomology, log étale cohomology, and log de Rham cohomology of log schemes over \(\mathbb{C}\)
• Decomposition into pairs-of-pants for complex algebraic hypersurfaces
• Homogeneous coordinate rings and mirror symmetry for toric varieties
• The Lefschetz theorem on hyperplane sections
• A GENERAL SMALL CANCELLATION THEORY
• The Coherent–Constructible Correspondence for Toric Deligne–Mumford Stacks
• Log Hodge groups on a toric Calabi-Yau degeneration
• Introduction to Toric Varieties. (AM-131)
• Logarithmic structures of Fontaine-Illusie. II
• Shellable Decompositions of Cells and Spheres.
• Combinatorial algebraic topology