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The Ax–Schanuel conjecture for variations of Hodge structures
We extend the Ax–Schanuel theorem recently proven for Shimura varieties by Mok–Pila–Tsimerman to all varieties supporting a pure polarizable integral variation of Hodge structures. In fact, Hodge
A global Torelli theorem for singular symplectic varieties
We systematically study the moduli theory of singular symplectic varieties which have a resolution by an irreducible symplectic manifold and prove an analog of Verbitsky's global Torelli theorem. In
The Kodaira dimension of complex hyperbolic manifolds with cusps
We prove a bound relating the volume of a curve near a cusp in a complex ball quotient $X=\mathbb{B}/\unicode[STIX]{x1D6E4}$ to its multiplicity at the cusp. There are a number of consequences: we
Higher rank stable pairs on K3 surfaces
TLDR
Higher rank analogs of Pandharipande-Thomas stable pair invariants in primitive classes for K3 surfaces are defined and computed and a "higher" KKV conjecture is proved by showing that the higher rank partition functions are modular forms.
A CLASSIFICATION OF LAGRANGIAN PLANES IN HOLOMORPHIC SYMPLECTIC VARIETIES
  • Benjamin Bakker
  • Mathematics
    Journal of the Institute of Mathematics of…
  • 23 October 2013
Classically, an indecomposable class $R$ in the cone of effective curves on a K3 surface $X$ is representable by a smooth rational curve if and only if $R^{2}=-2$ . We prove a higher-dimensional
Algebraic approximation and the decomposition theorem for Kähler Calabi–Yau varieties
We extend the decomposition theorem for numerically K-trivial varieties with log terminal singularities to the Kähler setting. Along the way we prove that all such varieties admit a strong locally
The global moduli theory of symplectic varieties
We develop the global moduli theory of symplectic varieties {in the sense of Beauville}. We prove a number of analogs of classical results from the smooth case, including a global Torelli theorem. In
o-minimal GAGA and a conjecture of Griffiths
We prove a conjecture of Griffiths on the quasi-projectivity of images of period maps using algebraization results arising from o-minimal geometry. Specifically, we first develop a theory of analytic
Lagrangian 4-planes in holomorphic symplectic varieties of K3[4]-type
We classify the cohomology classes of Lagrangian 4-planes ℙ4 in a smooth manifold X deformation equivalent to a Hilbert scheme of four points on a K3 surface, up to the monodromy action. Classically,
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