Related papers: Pseudoconvexity at infinity in Hodge theory: a cod…

Convex algebras, also called (semi)convex sets, are at the heart of modelling probabilistic systems including probabilistic automata. Abstractly, they are the Eilenberg-Moore algebras of the finitely supported distribution monad.…

By analyzing the local and infinitesimal behavior of degenerating polarized variations of Hodge structure the notion of infinitesimal variation of Hodge structure at infinity is introduced. It is shown that all such structures can be…

A basic problem in the geometry of degenerating period maps is to determine whether their completed images admit an intrinsic algebraic description. For polarized variations of Hodge structure over smooth quasi-projective surfaces, Deng and…

A recent theorem of [GGSM1] showed that adjoint orbits of semisimple Lie algebras have the structure of symplectic Lefschetz fibrations. We investigate the behaviour of their fibrewise compactifications. Expressing adjoint orbits and fibres…

The main purpose of this paper is to generalize the celebrated L${}^2$ extension theorem of Ohsawa-Takegoshi in several directions : the holomorphic sections to extend are taken in a possibly singular hermitian line bundle, the subvariety…

In convex geometry, the Blaschke surface area measure on the boundary of a convex domain can be interpreted in terms of the complexity of approximating polyhedra. In response to a question raised by D. Barrett, this approach is formulated…

The introduced notion of locally-periodic two-scale convergence allows to average a wider range of microstructures, compared to the periodic one. The compactness theorem for the locally-periodic two-scale convergence and the…

We generalize the finiteness theorem for the locus of Hodge classes with fixed self-intersection number, due to Cattani, Deligne, and Kaplan, from Hodge classes to self-dual classes. The proof uses the definability of period mappings in the…

We give a completion of the period map associated to a variation of polarized Hodge structure arising from a 2-dimensional geometric family that has Hodge type (1,2,2,1). This is the second known example of a completion of a period map that…

This paper concerns extension of maps using obstruction theory under a non classical viewpoint. It is given a classification of homotopy classes of maps and as an application it is presented a simple proof of a theorem by Adachi about…

We introduce the notion of a polyptych lattice, which encodes a collection of lattices related by piecewise linear bijections. We initiate a study of the new theory of convex geometry and polytopes associated to polyptych lattices. In…

The main purpose of this paper is to show that ideas of deformation theory can be applied to "infinite dimensional geometry". We develop the deformation theory of Brody curves. Brody curve is a kind of holomorphic map from the complex plane…

This is a part of our joint program. The purpose of this paper is to study smooth toroidal compactifications of Siegel varieties and their applications, we also try to understand the K\"ahler-Einstein metrics on Siegel varieties through the…

This paper studies Moore's measurable cohomology theory for locally compact groups and Polish modules. An elementary dimension-shifting argument is used to show that all classes in that theory have representatives with considerable extra…

We give an explicit lower bound, in terms of the distance from the boundary, for the Kobayashi metric of a certain class of bounded pseudoconvex domains in $\mathbb{C}^n$ with $\mathcal{C}^2$-smooth boundary using the regularity theory for…

We explore a notion of pseudofinite dimension, introduced by Hrushovski and Wagner, on an infinite ultraproduct of finite structures. Certain conditions on pseudofinite dimension are identified that guarantee simplicity or supersimplicity…

We prove an extension theorem for roots and logarithms of holomorphic line bundles across strictly pseudoconcave boundaries: they extend in all cases except one, when dimension and Morse index of a critical point is two. In that case we…

There are a number of examples of variations of Hodge structure of maximum dimension. However, to our knowledge, those that are global on the level of the period domain are totally geodesic subspaces that arise from an orbit of a subgroup…

We formulate a concrete geometric approximation hypothesis (Hypothesis~BB) asserting that codimension-$2$ Hodge classes on a smooth projective threefold can be realized as specializations of families whose general members are…

Let X be an irreducible complex variety, S a stratification of X and F a holomorphic vector bundle on the open statum. We give geometric conditions on S and F that produce a natural extension of the k-th Chern class F as a class in the…