38 citations · 101 across the 17 of their papers we have counts for
23 papers
Non-hyperbolicity of holomorphic symplectic varieties
Ljudmila Kamenova, Christian Lehn
We prove non-hyperbolicity of primitive symplectic varieties with that satisfy the rational SYZ conjecture. If in addition , we establish that the Kobayash…
Footnotes to the birational geometry of primitive symplectic varieties
Christian Lehn, Giovanni Mongardi, Gianluca Pacienza
In this note, we extend to the singular case some results on the birational geometry of irreducible holomorphic symplectic manifolds.
The monodromy of families of subvarieties on abelian varieties
Ariyan Javanpeykar, Thomas Krämer, Christian Lehn +1
Motivated by recent work of Lawrence-Venkatesh and Lawrence-Sawin, we show that non-isotrivial families of subvarieties in abelian varieties have big monodromy when twisted by gene…
The Morrison--Kawamata cone conjecture for singular symplectic varieties
Christian Lehn, Giovanni Mongardi, Gianluca Pacienza
We prove the Morrison--Kawamata cone conjecture for projective primitive symplectic varieties with $\Q$-factorial and terminal singularities with , from which we derive…
Deformations of rational curves on primitive symplectic varieties and applications
Christian Lehn, Giovanni Mongardi, Gianluca Pacienza
We study the deformation theory of rational curves on primitive symplectic varieties and show that if the rational curves cover a divisor, then, as in the smooth case, they deform…
Algebraic approximation and the decomposition theorem for Kähler Calabi-Yau varieties
Benjamin Bakker, Henri Guenancia, Christian Lehn
We extend the decomposition theorem for numerically -trivial varieties with log terminal singularities to the Kähler setting. Along the way we prove that all such varieties admi…
On the GHKS compactification of the moduli space of K3 surfaces of degree two
Klaus Hulek, Christian Lehn, Carsten Liese
We investigate a toroidal compactification of the moduli space of K3 surfaces of degree originating from the program formulated by Gross-Hacking-Keel-Siebert. This construction…
Algebraic Analysis of the Hypergeometric Function 1F1 of a Matrix Argument
Paul Görlach, Christian Lehn, Anna-Laura Sattelberger
In this article, we investigate Muirhead's classical system of differential operators for the hypergeometric function 1F1 of a matrix argument. We formulate a conjecture for the co…
The complex geometry of a hypothetical complex structure on
Christian Lehn, Sönke Rollenske, Caren Schinko
This article is a survey about or introduction to certain aspects of the complex geometry of a hypothetical complex structure on the six-sphere. We discuss a result of Peternell--C…
Geometric and Probabilistic Limit Theorems in Topological Data Analysis
Sara Kalisnik, Christian Lehn, Vlada Limic
We develop a general framework for the probabilistic analysis of random finite point clouds in the context of topological data analysis. We extend the notion of a barcode of a fini…
The global moduli theory of symplectic varieties
Benjamin Bakker, Christian Lehn
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 To…
A global Torelli theorem for singular symplectic varieties
Benjamin Bakker, Christian Lehn
We systematically study the moduli theory of symplectic varieties (in the sense of Beauville) which admit a resolution by an irreducible symplectic manifold. In particular, we prov…
Towards a symplectic version of the Chevalley restriction theorem
Michael Bulois, Christian Lehn, Manfred Lehn +1
If is a polar representation with Cartan subspace and Weyl group , it is shown that there is a natural morphism of Poisson schemes $\mathfrak c \oplus {\ma…
Stability of coisotropic fibrations on holomorphic symplectic manifolds
Christian Lehn, Gianluca Pacienza
We investigate the stability of fibers of coisotropic fibrations on holomorphic symplectic manifolds and generalize Voisin's result on Lagrangian subvarieties to this framework. We…
Twisted cubics on singular cubic fourfolds - On Starr's fibration
Christian Lehn
We study lines and twisted cubics on cubic fourfolds with simple isolated singularities. We show that the Hilbert scheme compactification of the total space of Starr's fibration on…
On the log minimal model program for irreducible symplectic varieties
Christian Lehn, Gianluca Pacienza
We show the termination of any log-minimal model program for a pair of a symplectic manifold and an effective -divisor .
Invariant deformation theory of affine schemes with reductive group action
Christian Lehn, Ronan Terpereau
We develop an invariant deformation theory, in a form accessible to practice, for affine schemes equipped with an action of a reductive algebraic group . Given the defining…
Twisted cubics on cubic fourfolds
Christian Lehn, Manfred Lehn, Christoph Sorger +1
We construct a new twenty-dimensional family of projective eight-dimensional irreducible holomorphic symplectic manifolds: the compactified moduli space M_3(Y) of twisted cubics on…
Base manifolds for Lagrangian fibrations on hyperkähler manifolds
Daniel Greb, Christian Lehn
We show that the base manifold of a Lagrangian fibration on a hyperkähler manifold is isomorphic to complex projective space. This generalises a theorem of J.-M. Hwang to the Kähle…
Normal crossing singularities and Hodge theory over Artin rings
Christian Lehn
We develop a Hodge theory for relative simple normal crossing varieties over an Artinian base scheme. We introduce the notion of a mixed Hodge structure over an Artin ring, which a…
Deformations of Lagrangian subvarieties of holomorphic symplectic manifolds
Christian Lehn
We generalize Voisin's theorem on deformations of pairs of a symplectic manifold and a Lagrangian submanifold to the case of Lagrangian normal crossing subvarieties. Partial result…
Lagrangian fibrations on hyperkähler fourfolds
Daniel Greb, Christian Lehn, Sönke Rollenske
Let X be a projective hyperkähler manifold containing a Lagrangian subtorus L. We study intersections of deformations of L, defining a canonical almost holomorphic map called L-red…
Lagrangian fibrations on hyperkähler manifolds - On a question of Beauville
Daniel Greb, Christian Lehn, Sönke Rollenske
Let X be a compact hyperkähler manifold containing a complex torus L as a Lagrangian subvariety. Beauville posed the question whether X admits a Lagrangian fibration with fibre L.…