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-2538 Canonical minimal models in numerical dimension one
- Math-2539 Canonical nonvanishing for smooth fourfolds
- Math-2540 The cohomological Hikita isomorphism for quivers
- Math-2541 Conditional good models for strongly Q-factorial Kähler fourfolds
- Math-2542 Kähler log abundance assuming logarithmic Iitaka
- Math-2543 Conditional abelianity for special half-weight fourfold pairs
- Math-2544 Existence of a finite ordinary Kähler fourfold program
- Math-2545 Generalized-canonical flip termination on Kähler fourfolds
- Math-2546 Generalized Hodge support on CM abelian varieties
- Math-2547 Generalized lc flip termination on Kähler fourfolds
- Math-2548 Minimal or Mori models for generalized rational lc pairs
- Math-2549 The generalized Mukai pseudoindex assertion
- Math-2550 Gepner-type numerical stability on quintic threefolds
- Math-2551 Rational Hodge classes on CM abelian varieties
- Math-2552 Hodge support on a specified K3 quadratic locus
- Math-2553 Hodge classes on generic abelian-cover Jacobian powers
- Math-2554 Hodge classes on diagonal complete-intersection powers
- Math-2555 Hodge classes on powers of split Weil sixfolds
- Math-2556 Rational Hodge classes on products of K3 surfaces
- Math-2557 Kähler fourfold abundance after nonvanishing
- Math-2558 B-semiampleness for compact Kähler log-smooth fibrations
- Math-2559 Numerical semiampleness of Kähler adjoints
- Math-2560 A geometric criterion for Kuga–Satake algebraicity
- Math-2561 Numerical-dimension-one log abundance in characteristic above three
- Math-2562 Logarithmic Kodaira additivity under stratum smoothness
- Math-2563 Maximal multipoint Seshadri constants in higher complex dimension
- Math-2564 Generic maximal Seshadri constants in positive characteristic
- Math-2565 Rational effectivity modulo a controlled boundary
- Math-2566 Topological right-triviality of constant-Milnor surface families
- Math-2567 Polynomiality of the natural invariant anticanonical index
- Math-2568 Zero Lelong numbers for minimal metrics on nef adjoints
- Math-2569 The Oka property for every complex K3 surface
- Math-2570 The ordinary-double-point normalized-volume gap
- Math-2571 The four-dimensional normalized-volume gap
- Math-2572 Virasoro constraints for projective complete intersections
- Math-2573 Completeness of original Pixton relations on closed moduli
- Math-2574 Prescribed large-volume stability charges on threefolds
- Math-2575 Bases of projective Lagrangian fibrations
- Math-2576 Numerical semiampleness of projective adjoints
- Math-2577 P=W for fixed-determinant trace-free coprime moduli
- Math-2578 Split tangents on rationally connected projective manifolds
- Math-2579 Schnell’s fiber-space assertion in Kodaira dimension zero
- Math-2580 Symmetry of bounded semialgebraic domains with compact quotient
- Math-2581 Classification of semialgebraic projective universal covers
- Math-2582 Removing a fixed pseudo-effective anticanonical error
- Math-2583 Invariant anticanonical sections under structure-sheaf acyclicity
- Math-2584 Invariant anticanonical sections with nonzero Euler characteristic
- Math-2585 Anticanonical nonvanishing from smooth semipositivity
- Math-2586 Two-step linear images of special quasi-projective groups
- Math-2587 Universal-cover products for integrable tangent summands