Product Information
Description
An annual survey of the math.AG arXiv category, covering research published from September 2025 – August 2026. Built on a close-reading set of 108 papers and organised into 40 chapters, it maps the year by the field's research sub-directions.
Book framework (share of the year's output):
- Algebraic Varieties and Moduli Spaces (64.4%) — Studies the geometry and classification of algebraic varieties, their moduli spaces, and related invariants such as bundles and cohomology.
- Cohomological and Geometric Structures (12.5%) — Explores cohomological theories, geometric structures, and their applications in algebraic geometry and related fields.
- Schemes, Morphisms, and Derived Categories (10.5%) — Investigates properties of schemes, morphisms, and derived categories, including affine and irreducible components.
- Stacks, Sheaves, and Derived Geometry (4.8%) — Focuses on stacks, sheaves, and derived categories, with applications to moduli problems and deformation theory.
- Tensors, Quotients, and Homological Algebra (2.2%) — Examines tensor products, quotient varieties, and homological invariants, including applications to representation theory and mirror symmetry.
- Singularities, Log Pairs, and Calabi-Yau (2.2%) — Studies singularities, log pairs, and Calabi-Yau varieties, including resolution and deformation aspects.
- Differential Operators and Modular Forms (1.9%) — Investigates differential operators, modular forms, and their connections to algebraic geometry and integrable systems.
- Toric Varieties and Fano Threefolds (0.9%) — Explores toric varieties, Fano threefolds, and related stability conditions and automorphisms.
- Computational and Tropical Methods (0.5%) — Develops computational algorithms and tropical techniques for solving problems in algebraic geometry.
Each sub-direction is covered across three chapters — how it framed its questions, the strength of its key findings, and its open debates and frontiers — so the reader gets a traceable picture of what this part of the field actually produced over the year.
