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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Proves that D^b(coh X) admits a full exceptional collection when X is a complex log del Pezzo surface with all singularities of type 1/3(1,1), including an explicit collection of length 13 for a degree-10 hypersurface example.
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.
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.
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