Related papers: A Generalization of Injective and Projective Compl…

We present the notion of injective hom-complexity, leading to a connection between the covering number of a group and the sectional number of a group homomorphism, and provide estimates for computing this invariant.

We propose a general definition of unprojection, and prove that it indeed generalizes previous efforts.

This paper generalize the idea of the authors in J. Pure Appl. Algebra 210 (2007) 437--445. Namely, we define and study a particular case of Gorenstein projective modules. We investigate some change of rings results for this new kind of…

This paper is a sequel to "T-structures and twisted complexes on derived injectives" by the same author with W. Lowen and M. Van den Bergh. We define a dg-category of unbounded twisted complexes on a dg-category, which is particularly…

Using techniques of projective geometry, we give elementary proofs of two theorems concerning Hagge configurations.

We solve the metrisability problem for generic three-dimensional projective structures.

We define and study complex structures and generalizations on spaces consisting of geodesics or harmonic maps that are compatible with the symmetries of these spaces. The main results are about existence and uniqueness of such structures.

After a review on the development of deformation theory of abelian complex structures from both the classical and generalized sense, we propose the concept of semi-abelian generalized complex structure. We present some observations on such…

This is a survey article on the recent developments of semipositivity, injectivity, and vanishing theorems for higher-dimensional complex projective varieties.

In this article we present a generalization of a Leibniz's geometrical theorem and an application of it.

We define generalized vector fields, and contraction and Lie derivatives with respect to them. Generalized commutators are also defined.

In generalized complex geometry, we revisit linear subspaces and submanifolds that have an induced generalized complex structure. We give an expression of the induced structure that allows us to deduce a smoothness criteria, we dualize the…

The aim of this article is to provide a complementary understanding to some results of the second author using the machinery of Koszul complexes, and to explain how this approach can provide a new description of projective derived…

An elementary approach to the construction of Coxeter group representations is presented.

The coordinate projective line over a field is seen as a groupoid with a further `projection' structure. We investigate conversely to what extent such an, abstractly given, groupoid may be coordinatized by a suitable field constructed out…

In this survey, we discuss whether the complex projective space can be characterized by its integral cohomology ring among compact complex manifolds.

The aim of the paper is to start to develop the most general theory of localizations/inversion. Several new concepts are introduced and studied.

We describe a notion of (abstract) projective line over a field as a set equipped with a certain first order structure, and a projectivity between projective lines as a bijection preserving this structure. The structure in question is that…

We study finite dimensional representations of the projective modular group. Various explicit dimension formulas are given.

Let R be a commutative ring and C a semidualizing R-module. In this article, we introduce and investigate the notion of DC-projective complexes. We first prove that a complex X is DC-projective if and only if each degree of X is a…