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The Ax–Schanuel conjecture for variations of Hodge structures
- Benjamin Bakker, Jacob Tsimerman
- MathematicsInventiones mathematicae
- 14 December 2017
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
- Benjamin Bakker, Christian Lehn
- Mathematics
- 23 December 2016
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
- Benjamin Bakker, Jacob Tsimerman
- MathematicsCompositio Mathematica
- 19 March 2015
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
- Benjamin Bakker, Andrei Jorza
- Mathematics, Computer Science
- 18 March 2011
TLDR
A CLASSIFICATION OF LAGRANGIAN PLANES IN HOLOMORPHIC SYMPLECTIC VARIETIES
- Benjamin Bakker
- MathematicsJournal 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…
Lagrangian hyperplanes in holomorphic symplectic varieties
- Benjamin Bakker, Andrei Jorza
- Mathematics
- 31 October 2011
Algebraic approximation and the decomposition theorem for Kähler Calabi–Yau varieties
- Benjamin Bakker, Henri Guenancia, Christian Lehn
- MathematicsInventiones mathematicae
- 1 December 2020
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
- Benjamin Bakker, Christian Lehn
- Mathematics
- 23 December 2018
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
- Benjamin Bakker, Yohan Brunebarbe, Jacob Tsimerman
- Mathematics
- 29 November 2018
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
- Benjamin Bakker, Andrei Jorza
- Mathematics
- 31 October 2011
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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