Related papers: Topologie des vari\'et\'es alg\'ebriques r\'eelles…
In this paper we construct Ulrich bundles of low rank on three-dimensional scrolls (with respect to the tautological line bundle). We pay special attention to the four types of threefold scrolls in $\mathbb{P}^5$ which were classified in…
Masuda (2008) provided the characterization of real Bott manifolds in terms of three operations on upper triangular matrices. We provide a combinatorial characterization of real Bott manifolds up to diffeomorphism in terms of operations on…
We prove an a priori estimate of type sup*inf on Riemannian manifold of dimension 3 (not necessarily compact).
The goal of this article is to survey recent developments in the theory of contact structures in dimension three.
This paper studies closed 3-manifolds which are the attractors of a system of finitely many affine contractions that tile $\mathbb{R}^3$. Such attractors are called self-affine tiles. Effective characterization and recognition theorems for…
We take a categorical approach to describe ternary derivations and ternary automorphisms of triangular algebras. New classes of automorphisms and derivations of triangular algebras are also introduced and studied.
We classify isotopy classes of automorphisms (self-homeomorphisms) of 3-manifolds satisfying the Thurston Geometrization Conjecture. The classification is similar to the classification of automorphisms of surfaces developed by Nielsen and…
After a historical discussion of classical uniformisation results for Riemann surfaces, of problems appearing in higher dimensions, and of uniformisation results for projective manifolds with trivial or ample canonical bundle, we introduce…
We show that if X is a smooth rationally connected threefold and C is a smooth projective curve then C can be embedded in X. Furthermore, a version of this property characterises rationally connected varieties of dimension at least 3. We…
Previous work of the authors studies minimal triangulations of closed 3-manifolds using a characterisation of low degree edges, embedded layered solid torus subcomplexes and 1-dimensional $\mathbb{Z}_2$-cohomology. The underlying blueprint…
Two conjectures relating the Kodaira dimension of a smooth projective variety and existence of number of nowhere vanishing 1-forms on the variety are proposed and verified in dimension 3.
We introduce and study a new 3d Topological Field Theory which can be associated to any compact real manifold X. This TFT is analogous to the 2d A-model and reduces to it upon compactification on an interval with suitable boundary…
Consider the smooth quadric Q_6 in P^7. The middle homology group H_6(Q_6,Z) is two-dimensional with a basis given by two classes of linear subspaces. We classify all threefolds of bidegree (1,p) inside Q_6.
In this paper we discuss the classification rank $3$ lattices preserved by finite orthogonal groups of isometries and derive from it the classification of regular polyhedra in the $3$-dimensional torus. This classification is highly related…
We give the classification of 3-dimensional Bol algebras associated to the trilinears operations $(e_2,e_3, e_2)=e_1, (e_2, e_3, e_3)=\pme_2$. It turn that for such trilinears operation there exist up to isomorphism and isotopy one family…
We show that there are algorithms to determine if a 3-manifold contains an essential lamination or a Reebless foliation.
We classify all 1-nodal degenerations of smooth Fano threefolds with Picard number 1 (both nonfactorial and factorial) and describe their geometry. In particular, we describe a relation between such degenerations and smooth Fano threefolds…
In this paper, we give a complete topological, as well as geometrical classification of closed 3-dimensional Lorentz manifolds admitting a noncompact isometry group.
A classification theorem is given of projective threefolds that are covered by a two-dimensional family of lines, but not by a higher dimensional family.
We classify three dimensional evolution algebras over a field having characteristic different from 2 and in which there are roots of orders 2, 3 and 7.