Algebraic geometry
Provisional editorial order for Top Open Problems: Millennium Prize Problems first, followed by assessed difficulty tiers; the unassessed remainder keeps its previous catalogue order. About rankings
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- Math-2192 The Tate Conjecture
- Math-2203 Abundance Conjecture
- Math-2236 Wikipedia geometry item 7: Fujita conjecture regarding the line bundle $K_{M} \otimes L^{\otimes m}$ constructed from a po…
- Math-2237 Wikipedia geometry item 13: Nagata's conjecture on curves, specifically the minimal degree required for a plane algebraic c…
- Math-2238 Wikipedia geometry item 14: Nagata–Biran conjecture that if $X$ is a smooth algebraic surface and $L$ is an ample line bund…
- Math-2239 Zariski multiplicity conjecture on the topological equisingularity and equimultiplicity of varieties at singular points
- Math-2263 Rationally connected irrational varieties with property (*)
- Math-2264 A transcendental-rank obstruction to surface hosts
- Math-2265 A cyclotomic resolution-Betti obstruction for the global canonical index
- Math-2314 Bounded Complements for $\varepsilon-Log-Canonical$ Varieties
- Math-2324 Bloch–Beilinson Torsion Conjecture for Albanese Kernels
- Math-2325 Nonvanishing or Uniruledness for Smooth Projective Varieties
- Math-2327 Affine Fibrations as Affine-Space Bundles
- Math-2328 Higher-Dimensional Cancellation for Affine Domains
- Math-2329 Stable Coordinate Conjecture for Complex Polynomials
- Math-2341 Algebraic Dimension and Reduction of Hyperkähler Manifolds
- Math-2351 Weak Zariski Decompositions of Pseudo-Effective Divisors
- Math-2360 Multipoint Seshadri Constants and Nagata-Type Conjectures
- Math-2369 Classification of Class-VII Complex Surfaces
- Math-2373 The Zariski Multiplicity Problem
- Math-2375 Log Abundance for Semi-Log-Canonical Pairs
- Math-2387 Dual-Graph Generation of Tautological Relations
- Math-2390 Lefschetz Classes and the Tate and Hodge Conjectures
- Math-2398 Fujita's Global Generation and Very-Ampleness Conjecture
- Math-2403 Abundance Conjecture for Projective Minimal Models
- Math-2404 Rational Curves on Compact Kähler Manifolds
- Math-2410 Bogomolov–Gieseker Inequality for Tilt-Semistable Threefold Complexes
- Math-2426 Finiteness of Atypical Hodge Subvarieties
- Math-2430 Finiteness of Optimal Points in Shimura Subvarieties
- Math-2434 Universal-Cover Decomposition for Nef Anticanonical Manifolds
- Math-2435 Kobayashi Pseudometric Vanishing on Calabi–Yau Manifolds
- Math-2445 Equivalence of Affine-Space Embeddings Under Automorphisms
- Math-2460 Nagata Conjecture for Multipoint Seshadri Constants
- Math-2461 Fujita's Conjecture for Effective Global Generation
- Math-2469 The Restricted Geometric Langlands Conjecture
- Math-2481 Known Cases of Iitaka Subadditivity
- Math-2494 The Generalized Étale-Homotopy Section Conjecture
- Math-2503 Torsion-Anomalous Conjecture for Semiabelian Varieties
- Math-2526 Algebraicity of the prescribed Kuga–Satake map
- Math-2527 Algebraicity of split Weil-type eightfold classes
- Math-2528 All ordinary Kähler klt fourfold programs terminate
- Math-2529 All rational-boundary projective lc fourfold programs terminate
- Math-2530 Rank-preserving contraction for anticanonical fibrations
- Math-2531 Integral Bloch statement for surfaces of geometric genus zero
- Math-2532 Arithmetic Stein-degree bounds for log Calabi–Yau boundaries
- Math-2533 Bounded local klt complements for Fano contractions
- Math-2534 Bounded-metric anticanonical nonvanishing for klt pairs
- Math-2535 Bounded denominators in low-dimensional log Calabi–Yau fibrations
- Math-2536 Campana–Peternell for Fano sixfolds
- Math-2537 Abelianity of special compact Kähler fundamental groups