63 citations · 215 across the 20 of their papers we have counts for
14 papers · 1 filter
Universal affine bundles for compact complex manifolds
Simion Filip, Valentino Tosatti
We construct a universal affine bundle over a compact complex manifold equipped with a probability measure , which is affine over the vector space $H_{1,1}(X;\mathbb{R})…
Nonlinearizable embeddings of elliptic curves in rational surfaces
Simion Filip, Valentino Tosatti
We show that for any smooth cubic in , there exists a dense set of configurations of 9 distinct points such that blowing up at these 9 points, th…
Gaps in the support of canonical currents on projective K3 surfaces
Simion Filip, Valentino Tosatti
We construct examples of canonical closed positive currents on projective K3 surfaces that are not fully supported on the complex points. The currents are the unique positive repre…
Canonical currents and heights for K3 surfaces
Simion Filip, Valentino Tosatti
We construct canonical positive currents and heights on the boundary of the ample cone of a K3 surface. These are equivariant for the automorphism group and fit together into a con…
Tropical Dynamics of Area-Preserving Maps
Simion Filip
We consider a class of area-preserving, piecewise affine maps on the 2-sphere. These maps encode degenerating families of K3 surface automorphisms and are profitably studied using…
Kummer rigidity for K3 surface automorphisms via Ricci-flat metrics
Simion Filip, Valentino Tosatti
We give an alternative proof of a result of Cantat and Dupont, showing that any automorphism of a K3 surface with measure of maximal entropy in the Lebesgue class must be a Kummer…
Notes on the Multiplicative Ergodic Theorem
Simion Filip
The Oseledets Multiplicative Ergodic theorem is a basic result with numerous applications throughout dynamical systems. These notes provide an introduction to this theorem, as well…
The algebraic hull of the Kontsevich-Zorich cocycle
Alex Eskin, Simion Filip, Alex Wright
We compute the algebraic hull of the Kontsevich-Zorich cocycle over any GL^+_2(R) invariant subvariety of the Hodge bundle, and derive from this finiteness results on such subvarie…
Quaternionic covers and monodromy of the Kontsevich-Zorich cocycle in orthogonal groups
Simion Filip, Giovanni Forni, Carlos Matheus
We give an example of a Teichmüller curve which contains, in a factor of its monodromy, a group which was not observed before. Namely, it has Zariski closure equal to the group $SO…
Families of K3 surfaces and Lyapunov exponents
Simion Filip
Consider a family of K3 surfaces over a hyperbolic curve (i.e. Riemann surface). Their second cohomology groups form a local system, and we show that its top Lyapunov exponent is a…
Zero Lyapunov exponents and monodromy of the Kontsevich-Zorich cocycle
Simion Filip
We describe all the situations in which the Kontsevich-Zorich cocycle has zero Lyapunov exponents. Confirming a conjecture of Forni, Matheus, and Zorich, this only occurs when the…
On Hoelder-continuity of Oseledets subspaces
Vitor Araujo, Alexander I. Bufetov, Simion Filip
For Hoelder cocycles over a Lipschitz base transformation, possibly non-invertible, we show that the subbundles given by the Oseledets Theorem are Hoelder-continuous on compact set…
Splitting mixed Hodge structures over affine invariant manifolds
Simion Filip
We prove that affine invariant manifolds in strata of flat surfaces are algebraic varieties. The result is deduced from a generalization of a theorem of Möller. Namely, we prove th…
Semisimplicity and rigidity of the Kontsevich-Zorich cocycle
Simion Filip
We prove that invariant subbundles of the Kontsevich-Zorich cocycle respect the Hodge structure. In particular, we establish a version of Deligne semisimplicity in this context. Th…