Related papers: Linear spaces of rational integrable 1-forms
The space of codimension one holomorphic foliations of degree 1 in a projective space has an irreducible component whose general element is a logarithmic differential 1-form with simple poles in three hyperplanes. We compute its projective…
The object of this note is the moduli spaces of cubic fourfolds (resp., Gushel-Mukai fourfolds) which contain some special rational surfaces. Under some hypotheses on the families of such surfaces, we develop a general method to show the…
The convenient setting for smooth mappings, holomorphic mappings, and real analytic mappings in infinite dimension is sketched. Infinite dimensional manifolds are discussed with special emphasis on smooth partitions of unity and tangent…
We determine the structure of the singular locus of generic codimension-$q$ logarithmic foliations and its relation with the unfoldings of said foliations. In the case where the ambient variety is the projective space $\mathbb{P}^n$ we…
We construct a smooth complex projective rational surface with infinitely many mutually non-isomorphic real forms. This gives the first definite answer to a long standing open question if a smooth complex projective rational surface has…
We consider the locus of irreducible nonsingular rational curves of degree d Pn, n>2, meeting a generic collection of linear subspaces. When this locus is 0 (resp 1)- dimensional, we compute (recursively) its degree (resp. geometric genus).…
We survey some results on real rational surfaces focused on their topology and their birational geometry.
In this article we study polynomial logarithmic $q$-forms on a projective space and characterize those that define singular foliations of codimension $q$. Our main result is the algebraic proof of their infinitesimal stability when $q=2$…
We use a function field version of the Hardy-Littlewood circle method to study the locus of free rational curves on an arbitrary smooth projective hypersurface of sufficiently low degree. On the one hand this allows us to bound the…
We describe some results on moduli space of logarithmic connections equipped with framings on a $n$-pointed compact Riemann surface.
We study codimension one holomorphic foliations on complex projective spaces and compact manifolds under the assumption that the foliation has a projective transverse structure in the complement of some invariant codimension one analytic…
In this paper we use finite vector spaces (finite dimension, over finite fields) as a non-standard computational model of linear logic. We first define a simple, finite PCF-like lambda-calculus with booleans, and then we discuss two finite…
This paper is devoted to characterizing complex projective structures defined on Riemann surface orbifolds and giving rise to injective developing maps defined on the monodromy covering of the surface (orbifold) in question. The relevance…
We endow the set of complements of a fixed subspace of a projective space with the structure of an affine space, and show that certain lines of such an affine space are affine reguli or cones over affine reguli. Moreover, we apply our…
Using several numerical invariants, we study a partition of the space of line arrangements in the complex projective plane, given by the intersection lattice types. We offer also a new characterization of the free plane curves using the…
We construct the moduli space of r-jets at a point of Riemannian metrics on a smooth manifold. The construction is closely related to the problem of classification of jet metrics via differential invariants. The moduli space is proved to be…
In this paper we introduce the concept of infinite pointwise dense lineability (spaceability), and provide a criterion to obtain density from mere lineability. As an application, we study the linear and topological structures within the set…
It is shown that moduli spaces of complete families of compact complex hypersurfaces in complex manifolds often come equipped canonically with projective structures satisfying some natural integrability conditions.
Projective spaces for finite-dimensional vector spaces over general fields are considered. The geometry of these spaces and the theory of line bundles over these spaces is presented. Particularly, the space of global regular sections of…
We classify the rational differential 1-forms with simple poles and simple zeros on the Riemann sphere according to their isotropy group; when the 1-form has exactly two poles the isotropy group is isomorphic to $\mathbb{C}^{*}$, namely…