Constructs infinitely many new klt Q-Gorenstein degenerations of P^n via weighted projective spaces in any dimension and studies deformations of weighted projective threefolds.
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17 Pith papers cite this work, alongside 2,361 external citations. Polarity classification is still indexing.
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The Artin invariant of a smooth K3 hypersurface is characterized in terms of quasi-F-splitting, yielding an explicit formula.
Affine closure of T*O_n in sl_n is isomorphic via C*-Hamiltonian reduction to the minimal nilpotent orbit closure in so_{2n+2}, and has no symplectic resolution.
Classification of terminalizations of symplectic quotients of K3^{[n]} and generalized Kummer varieties yields at least nine new deformation types of irreducible symplectic varieties of dimension four.
Cyclically pure subrings of Du Bois singularities are Du Bois over Q-algebras, with new results even for faithfully flat maps.
Constructs non-projective complete log canonical surfaces with semi-ample canonical divisors for Kodaira dimensions 0/1/2 and proves automatic projectivity when Kodaira dimension is minus infinity.
Develops a method for plus-pure thresholds and classifies BCM-regular diagonal hypersurfaces in mixed characteristic (0,2) via necessary/sufficient conditions and lower bounds.
α(X,Δ,L) and δ(X,Δ,L) are computed by quasi-monomial valuations for projective klt pairs over algebraically closed fields of char 0, without uncountability assumptions.
The visible spectrum of poles of the local zeta function of an analytic ideal is recovered recursively from the asymptotic expansion of its sublevel-set volume, with multiplicities and coefficients.
Proves canonical map degree ≤72 for such threefolds when p_g>243, with equality only if Albanese fiber is a specific surface of general type with p_g=3, q=0, K_F²=36 and canonical degree 36; improves Cai's prior bound.
Canonical stacks of log del Pezzo surfaces with only 1/3(1,1) singularities admit explicit full exceptional collections of length 12-K_X^2+4r/3, with a length-13 collection for X10.
Generalizes positivity theorems of Popa-Wu and Popa-Schnell for Hodge modules and Higgs bundles to smooth proper DM stacks admitting projective coarse moduli spaces.
Under a codimension assumption on the singular locus, isomorphism of the m-th differential sheaf implies isomorphisms for all lower i on complex hypersurfaces, with a positive characteristic analogue discussed.
Alternative proof of anticanonical MMP existence for potentially klt pairs under birational Zariski decomposition assumption, together with a lifting structure theorem for partial MMP steps.
Proves optimal Kawamata-Miyaoka inequality for terminal Q-Fano threefolds of index >=3 and derives c1^3 < 3 c2 c1 for all such threefolds.
Coxeter symmetries from isomorphic flops in Kähler-favorable CICYs make the 4D N=2 prepotential solve the Helmholtz equation on the moduli space, enabling resummed expressions from worldsheet instantons.
The normalized local volume of a non-closed point equals an expression built from the normalized local volumes of closed points.
citing papers explorer
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Weighted projective degenerations of $\mathbb{P}^{n}$
Constructs infinitely many new klt Q-Gorenstein degenerations of P^n via weighted projective spaces in any dimension and studies deformations of weighted projective threefolds.
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An explicit formula for the Artin invariant of smooth K3 hypersurfaces
The Artin invariant of a smooth K3 hypersurface is characterized in terms of quasi-F-splitting, yielding an explicit formula.
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A connection between minimal nilpotent orbits of types A and D via Hamiltonian reduction
Affine closure of T*O_n in sl_n is isomorphic via C*-Hamiltonian reduction to the minimal nilpotent orbit closure in so_{2n+2}, and has no symplectic resolution.
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Terminalizations of quotients of compact hyperk\"ahler manifolds by induced symplectic automorphisms
Classification of terminalizations of symplectic quotients of K3^{[n]} and generalized Kummer varieties yields at least nine new deformation types of irreducible symplectic varieties of dimension four.
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Pure subrings of Du Bois singularities are Du Bois singularities
Cyclically pure subrings of Du Bois singularities are Du Bois over Q-algebras, with new results even for faithfully flat maps.
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Non-projective complete log canonical surfaces
Constructs non-projective complete log canonical surfaces with semi-ample canonical divisors for Kodaira dimensions 0/1/2 and proves automatic projectivity when Kodaira dimension is minus infinity.
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BCM-regularity of diagonal hypersurfaces and plus-pure thresholds in mixed characteristic
Develops a method for plus-pure thresholds and classifies BCM-regular diagonal hypersurfaces in mixed characteristic (0,2) via necessary/sufficient conditions and lower bounds.
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On the quasi-monomiality of the $\alpha$- and $\delta$-invariants
α(X,Δ,L) and δ(X,Δ,L) are computed by quasi-monomial valuations for projective klt pairs over algebraically closed fields of char 0, without uncountability assumptions.
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On the Divisorial Geometry of Volume Asymptotics of Sublevel Sets
The visible spectrum of poles of the local zeta function of an analytic ideal is recovered recursively from the asymptotic expansion of its sublevel-set volume, with multiplicities and coefficients.
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On the canonical degree of a Gorenstein minimal threefold of general type
Proves canonical map degree ≤72 for such threefolds when p_g>243, with equality only if Albanese fiber is a specific surface of general type with p_g=3, q=0, K_F²=36 and canonical degree 36; improves Cai's prior bound.
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Exceptional collections for canonical stacks of log del Pezzo surfaces with $\frac13(1,1)$ singularities
Canonical stacks of log del Pezzo surfaces with only 1/3(1,1) singularities admit explicit full exceptional collections of length 12-K_X^2+4r/3, with a length-13 collection for X10.
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Positivity in the context of Hodge modules and Higgs bundles on Deligne-Mumford stacks
Generalizes positivity theorems of Popa-Wu and Popa-Schnell for Hodge modules and Higgs bundles to smooth proper DM stacks admitting projective coarse moduli spaces.
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Higher singularities for hypersurfaces
Under a codimension assumption on the singular locus, isomorphism of the m-th differential sheaf implies isomorphisms for all lower i on complex hypersurfaces, with a positive characteristic analogue discussed.
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Structure of the Anticanonical Minimal Model Program for Potentially klt Pairs
Alternative proof of anticanonical MMP existence for potentially klt pairs under birational Zariski decomposition assumption, together with a lifting structure theorem for partial MMP steps.
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Kawamata-Miyaoka-type inequality for $\mathbb Q$-Fano varieties with canonical singularities II: Terminal $\mathbb Q$-Fano threefolds
Proves optimal Kawamata-Miyaoka inequality for terminal Q-Fano threefolds of index >=3 and derives c1^3 < 3 c2 c1 for all such threefolds.
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Kaleidoscopes, Waves and the Prepotential
Coxeter symmetries from isomorphic flops in Kähler-favorable CICYs make the 4D N=2 prepotential solve the Helmholtz equation on the moduli space, enabling resummed expressions from worldsheet instantons.
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On the normalized local volume of a non-closed point
The normalized local volume of a non-closed point equals an expression built from the normalized local volumes of closed points.