Related papers: Projective contact log varieties

Complex contact manifolds arise naturally in differential geometry, algebraic geometry and exterior differential systems. Their classification would answer an important question about holonomy groups. The geometry of such manifold $X$ is…

The purpose of this largely expository note is to give some examples of smooth projective varieties with zero first Betti number but nontrivial families of local systems of higher ranks. The most interesting examples are due to Simpson.

We prove that the infinitesimal variations of Hodge structure arising in a number of geometric situations are non-generic. In particular, we consider the case of generic hypersurfaces in complete smooth projective toric varieties, generic…

We introduce the notion of a regular integrable connection on a smooth log scheme over $\mathbf{C}$ and construct an equivalence between the category of such connections and the category of integrable connections on its analytification,…

In this note we study curves (arrangements) in the complex projective plane which can be considered as generalizations of free curves. We construct families of arrangements which are nearly free and possess interesting geometric properties.…

Projective varieties with ample cotangent bundle satisfy many notions of hyperbolicity, and one goal of this paper is to discuss generalizations to quasi-projective varieties. A major hurdle is that the naive generalization fails, i.e. the…

In this article we address the existence of positive loops of contactomorphisms in overtwisted contact 3-folds. We present a construction of such positive loops in the contact fibered connected sum of certain contact 3-folds along…

We define a family of symplectic invariants which obstruct exact symplectic embeddings between Liouville manifolds, using the general formalism of linearized contact homology and its L-infinity structure. As our primary application, we…

In this survey, we give an overview of Brieskorn manifolds and varieties, and their role in contact topology. We discuss open books, fillings and invariants such as contact and symplectic homology. We also present some new results involving…

This paper gives a foundation of log smooth deformation theory. We study the infinitesimal liftings of log smooth morphisms and show that the log smooth deformation functor has a representable hull. This deformation theory gives, for…

We construct correspondences in logarithmic Hodge theory over a perfect field of arbitrary characteristic. These are represented by classes in the cohomology of sheaves of differential forms with log poles and, notably, log zeroes on…

This is the first of the two articles where we determine the higher smooth surgery structure sets of complex projective spaces (up to some extension problems) and the forgetful map to their topological versions in low dimensions. In this…

We establish that smooth, geometrically integral projective varieties of small degree are not pointless in suitable solvable extensions of their field of definition, provided that this field is algebraic over $\Bbb Q$.

We propose to study homomorphisms of connectome graphs. Homomorphisms can be studied as sequences of elementary homomorphisms - folds, which identify pairs of vertices. Several fold types are defined. Initial computation results for some…

In this paper we define a functor-- leveled sub-cohomology. (It bears no relation with the level of elliptic curves). It is based on leveled cycles on a smooth projective variety, and will be expected to reveal a structure in the level.

A Jacobi structure $J$ on a line bundle $L\to M$ is weakly regular if the sharp map $J^\sharp : J^1 L \to DL$ has constant rank. A generalized contact bundle with regular Jacobi structure possess a transverse complex structure. Paralleling…

We provide a classification of $ts$-invariant sub-Lorentzian structures on $3$ dimensional contact Lie groups. Our approach is based on invariants arising form the construction of a normal Cartan connection.

In this note, we consider contractible loops of contactomorphisms that are positive over some non-empty closed subset of a contact manifold. Such closed subsets are called immaterial. We argue that the complement of a Reeb-invariant…

This article is a continuation of a previous article which concerned the splitting problem for subspaces of superspaces. We begin with a general account of projective superspaces. Subsequently, we specialise to subvarieties of `positive'…

Any smooth projective variety contains many complete intersection subvarieties with ample cotangent bundles, of each dimension up to half its own dimension.