Algebraic Geometry
-
0 votes 0 replies 2 views
Paper Termination of projective and Kähler fourfold minimal model programs
Proves termination of every existing generalized log canonical flip sequence on globally Weil ℚ-factorial compact Kähler fourfolds, with rational boundary, fixed rational analytically nef b-data, and projective small…
-
0 votes 0 replies 0 views
Paper Numerical semiampleness and generalized minimal models
Proves numerical semiampleness for nef adjoints KX+B+M with KX+B pseudo-effective and M nef rational, for projective klt rational pairs over algebraically closed characteristic-zero fields and smooth compact…
-
0 votes 0 replies 0 views
Paper Log abundance for compact Kähler spaces under logarithmic Iitaka subadditivity
Using logarithmic Iitaka subadditivity, proves log abundance in every dimension for normal compact Kähler log canonical pairs with effective rational boundary: an analytically nef ℚ-Cartier adjoint is semiample. It also…
-
0 votes 0 replies 0 views
Paper The rational Hodge conjecture for CM abelian varieties
Proves the rational Hodge conjecture for every complex CM abelian variety, in every dimension and codimension. Through Milne's theorems, this also gives the Tate conjecture for all abelian varieties over finite fields…
-
0 votes 0 replies 0 views
Paper Virasoro constraints for complete intersections and projective-bundle towers
Proves the full ordinary unreduced descendant Virasoro conjecture for smooth complete intersections in complex projective space, in every genus and curve class with arbitrary cohomology insertions. The constraints also…
-
0 votes 0 replies 0 views
Paper Fundamental groups of special complex varieties and root orbifolds
Proves Campana's abelianity conjecture: special compact Kähler manifolds have virtually abelian fundamental groups. Using this theorem, establishes the same conclusion for order-two root orbifolds of smooth projective…
-
0 votes 0 replies 0 views
Paper A stable-coordinate counterexample in four variables
Constructs a polynomial in four complex variables that is not a coordinate but becomes one after adjoining a single variable, disproving the Stable Coordinate conjecture in four variables. Every fiber is affine…
-
0 votes 0 replies 0 views
Paper Log-canonical threefold abundance in numerical dimension one
Proves log abundance for projective log canonical threefold pairs over algebraically closed fields of characteristic p > 3 when the effective boundary is rational and the ℚ-Cartier adjoint is nef of numerical…
-
0 votes 0 replies 0 views
Paper Nagata’s conjecture and maximal Seshadri constants
Proves Nagata's strict inequality \sumi mi\lt d\sqrt r for every nonzero effective plane curve of degree d through r ≥ 10 very general complex points, with arbitrary multiplicities mi. It also proves maximal…
-
0 votes 0 replies 0 views
Paper Shafarevich counterexamples in dimension two and with large fundamental group
Constructs a smooth projective complex fourfold with large fundamental group whose universal cover contains no positive-dimensional compact analytic subvariety but is neither Stein nor holomorphically convex. A separate…
-
0 votes 0 replies 0 views
Paper Global quantum geometric Langlands at irrational level
Proves the unramified de Rham quantum geometric Langlands equivalence for every connected simple complex algebraic group on every smooth projective connected complex curve, at every shifted level $`c\in\mathbb…
-
0 votes 0 replies 0 views
Paper Counterexamples to Zariski’s multiplicity conjecture
Disproves Zariski's multiplicity conjecture by constructing reduced holomorphic hypersurface germs that are ambiently homeomorphic but have different multiplicities. The examples include hypersurfaces in ℂ4 with…
-
0 votes 0 replies 0 views
Paper Iitaka subadditivity, variation, and logarithmic additivity
Proves Campana's orbifold Iitaka subadditivity conjecture for smooth Fujiki-class-\mathcal C manifolds with rational simple-normal-crossing boundaries. For projective fibrations f:U\to V of smooth complex…
-
0 votes 0 replies 0 views
Paper Anticanonical nonvanishing in every dimension
If X is a smooth connected complex projective variety and -KX admits a smooth Hermitian metric with nonnegative curvature, then H^0(X,-mKX)\ne0 for some m > 0. Thus smooth semipositivity forces a nonzero…
-
0 votes 0 replies 0 views
Paper Bounded klt complements for Fano contractions
Proves the finite-rational-coefficient form of Shokurov’s bounded-klt-complement conjecture for ϵ-lc complex Fano-type pairs with nef anti-log-canonical divisor. For ϵ-lc Fano contractions over any algebraically closed…
-
0 votes 0 replies 0 views
Paper The Campana–Peternell conjecture in dimension six
Proves the Campana–Peternell conjecture in complex dimension six: every smooth connected complex projective Fano sixfold with nef tangent bundle is rational homogeneous. Manuscript September 25, 2026 · · cite as…
-
0 votes 0 replies 0 views
Paper P = W for fixed-determinant \mathrm{SL}_{n} moduli spaces
Proves Pk=W{2k}=W{2k+1} on the full rational cohomology of smooth coprime fixed-determinant, trace-free Higgs moduli spaces and their character varieties for composite ranks over smooth projective complex curves of…
-
0 votes 0 replies 0 views
Paper The ordinary-double-point volume gap
Proves the ordinary-double-point volume-gap conjecture: every singular complex algebraic klt germ of dimension n ≥ 2, with zero boundary, has normalized volume at most 2(n-1)^n. Equality holds precisely for an…
-
0 votes 0 replies 0 views
Paper The equivariant cohomological Hikita conjecture
Proves the equivariant cohomological Hikita correspondence for every finite quiver, including loops and multiple arrows, with arbitrary dimension and framing vectors and commuting flavor torus. When every semistable…
-
0 votes 0 replies 0 views
Paper A counterexample to Griffiths’ positivity conjecture
Constructs ample rank-two bundles on \mathbb P^1\times\mathbb P^1 with no smooth Hermitian metric of strictly Griffiths-positive curvature, disproving Griffiths' positivity conjecture already on the quadric surface.…
-
0 votes 0 replies 0 views
Paper A counterexample to Pixton completeness in Chow
Constructs a tautological relation on a moduli space of stable pointed curves that vanishes in rational Chow, hence in rational cohomology, but lies outside Pixton's original relation span. This disproves the Chow and…
-
0 votes 0 replies 0 views
Paper Irrational cubic fourfolds with Hodge-theoretic and categorical K3 associations
For every sufficiently large admissible Hassett discriminant, a very general smooth complex cubic fourfold is irrational despite having both an untwisted geometric K3 category and an integral Hodge-theoretic K3…
-
0 votes 0 replies 0 views
Paper Gepner symmetry and large-volume stability on threefolds
Proves Toda's Gepner conjecture for every smooth complex quintic threefold, constructing a numerical Bridgeland stability condition with the prescribed phase shift 2/5. Also constructs numerical Bridgeland stability…
-
0 votes 0 replies 0 views
Paper Semialgebraic universal covers and bounded domains
Proves the Kollár–Pardon conjecture: the semialgebraic universal covers of connected normal projective complex varieties are exactly products D\times\mathbb C^m\times F, with D bounded symmetric and F simply…
-
0 votes 0 replies 0 views
Paper The Global Spherical Shell conjecture
Every connected minimal compact complex surface of class VII with b2\gt 0 contains a global spherical shell, proving the positive-b2 Global Spherical Shell conjecture. Such a shell is a holomorphically embedded…
-
0 votes 0 replies 0 views
Paper The generalized Mukai conjecture
Proves the generalized Mukai conjecture: every positive-dimensional smooth complex projective Fano manifold of dimension n, Picard number ρ and pseudoindex ι satisfies \rho(\iota-1)\le n, with equality exactly for…
-
0 votes 0 replies 0 views
Paper Topological triviality of \mu-constant surface singularities
Proves topological right-triviality for every holomorphic one-parameter family of isolated hypersurface singularities in ℂ3 with constant Milnor number, resolving the surface case of the μ-constant problem. After…
-
0 votes 0 replies 0 views
Paper Bloch’s conjecture for complex surfaces
Proves Bloch's conjecture: for every smooth connected projective complex surface S with pg(S)=0, the Albanese map \mathrm{CH}0(S)^0\to\mathrm{Alb}(S)(\mathbb C) on integral degree-zero zero-cycles is an…
-
0 votes 0 replies 0 views
Paper Kobayashi’s canonical-ampleness conjecture
Every compact connected Kähler manifold of positive complex dimension with no nonconstant entire curve has ample canonical bundle and is therefore projective. This proves Kobayashi's canonical-ampleness conjecture in…
-
0 votes 0 replies 0 views
Paper Tangent splittings and product decompositions
A splitting of the tangent bundle of a compact Kähler manifold into two integrable holomorphic subbundles induces a compatible product decomposition of its universal cover, proving the two-summand form of Beauville's…
36 posts