Related papers: Leaf schemes and Hodge loci
We discuss various problems regarding the structure of the foliation of some foliated submanifolds S of C^n, in particular Levi flat ones. As a general scheme, we suppose that S is bounded along a coordinate (or a subset of coordinates),…
The paper gives a categorical approach to generalized manifolds such as orbit spaces and leaf spaces of foliations. It is suggested to consider these spaces as sets equipped with some additional structure which generalizes the notion of…
Species tree estimation is a complex problem, due to the fact that different parts of the genome can have different evolutionary histories than the genome itself. One of the causes for this discord is incomplete lineage sorting (also called…
In the recent works of a number of people there has emerged a beautiful new perspective on the arithmetic properties of Hodge structures. A central result in that development appears in a paper by Baldi, Klingler, and Ullmo. In this…
One of the main virtues of trees is to represent formal solutions of various functional equations which can be cast in the form of fixed point problems. Basic examples include differential equations and functional (Lagrange) inversion in…
The purpose of this paper is to study the structure and the algebraic varieties of Hom-associative algebras. We give characterize multiplicative simple Hom-associative algebras and show some examples deforming the $2\times 2$-matrix algebra…
A way to characterize the space of leaves of a foliation in terms of connections is proposed. A particular example of vertex algebra cohomology of codimension one foliations on complex curves is considered.
Although contemporary model theory has been called "algebraic geometry minus fields", the formal methods of the two fields are radically different. This dissertation aims to shrink that gap by presenting a theory of logical schemes,…
We describe the topological types of leaves of generic logarithmic foliations on the complex projective plane. We prove that all leaves, except for a finite many are biholomorphic to $\mathbb{C}$ or homeomorphic to the surface known as Loch…
We study the homotopy theory of a certain type of diagram categories whose vertices are in variable categories with a functorial path, leading to a good calculation of the homotopy category in terms of cofibrant objects. The theory is…
An important result for regular foliations is their formal semi-local triviality near simply connected leaves. We extend this result to singular foliations for all 2-connected leaves and a wide class of 1- connected leaves by proving a…
This is a paper in a series that studies smooth relative Lie algebra homologies and cohomologies based on the theory of formal manifolds and formal Lie groups. In three previous papers, we introduce the notion of formal manifolds and study…
We study those real $\mathcal{C}^\infty$ foliations in complex surfaces whose leaves are holomorphic curves. The main motivation is to try and understand these foliations in neighborhoods of curves: can we expect the space of foliations in…
The purpose of this paper is to present a ``Cech-De Rham'' model for the cohomology of leaf spaces. This model lends itself to the construction of characteristic classes (in the cohomology of classifying spaces) by explicit geometrical…
We begin by introducing the concept of a Hodge structure and give some of its basic properties, including the Hodge and Lefschetz decompositions. We then define the period map, which relates families of Kahler manifolds to the families of…
In this paper, we establish an innovative framework in logarithmic Hodge theory for toroidal varieties, introducing weighted toroidal structures and developing a systematic obstruction theory for Hodge classes. Building upon recent advances…
This paper is the first in a series. The main goal of the series is to present a geometric construction of certain remarkable tensor categories arising from quantum groups coresponding to the value of deformation parameter $q$ equal to a…
In this article, we pursue two main objectives. The first is to show that the fundamental results of Green-Lazarsfeld (1987, 1991) on generic vanishing theorems, and works of Budur-Wang (2015, 2020) on cohomology jumping loci, can be…
In this article we introduce algorithms which compute iterations of Gauss-Manin connections, Picard-Fuchs equations of Abelian integrals and mixed Hodge structure of affine varieties of dimension $n$ in terms of differential forms. In the…
This paper contributes to the solution of the Poincare problem, which is to bound the degree of a (generalized algebraic) leaf of a (singular algebraic) foliation of the complex projective plane. The first theorem gives a new sort of bound,…