Related papers: Finite schemes and secant varieties over arbitrary…

Convergence and normal continuity analysis of a bivariate non-stationary (level-dependent) subdivision scheme for 2-manifold meshes with arbitrary topology is still an open issue. Exploiting ideas from the theory of asymptotically…

This paper obtains criteria for a Fano variety X with normal crossing singularities defined over an algebraically closed field of characteristic zero, to be smoothable. The difference with the original version is that the theory of…

If $S$ is a scheme of characteristic $p$, we define an $F$-zip over $S$ to be a vector bundle with two filtrations plus a collection of semi-linear isomorphisms between the graded pieces of the filtrations. For every smooth proper morphism…

We consider the question of which zero-dimensional schemes deform to a collection of distinct points; equivalently, we ask which Artinian k-algebras deform to a product of fields. We introduce a syzygetic invariant which sheds light on this…

The finite basis property is often connected with the finite rank property, which it entails. Many examples have been produced of finite rank varieties which are not finitely based. In this note, we establish a result on nilpotent…

The schematic finite spaces are those finite ringed spaces where a theory of quasi-coherent modules can be developed with minimal natural conditions. We give various characterizations of these spaces and their natural morphisms. We show…

In this note we present a notion of fundamental scheme for Cohen- Macaulay, order 1, irreducible congruences of lines. We show that such a congruence is formed by the k-secant lines to its fundamental scheme for a number k that we call the…

Let $X$ be an integral scheme of finite presentation over a perfect field. Let $q$ be a singular closed point of $X$. We prove that there exists an open subset $V$ of $X$ containing $q$ such that $V$ admits a resolution, that is, there…

In this paper we discuss different properties of noncommutative schemes over a field. We define a noncommutative scheme as a differential graded category of a special type. We study regularity, smoothness and properness for noncommutative…

The goal of this work is to study geometric properties of geometrically irreducible subschemes on degenerations of Fano varieties (more generally, of separably rationally connected varieties). It is known that these geometrically…

We study when a smooth variety $X$, embedded diagonally in its Cartesian square, is the zero scheme of a section of a vector bundle of rank $\dim(X)$ on $X\times X$. We call this the diagonal property (D). It was known that it holds for all…

We give an overview of invariants of algebraic singularities over perfect fields. We then show how they lead to a synthetic proof of embedded resolution of singularities of 2-dimensional schemes.

In this article we extend Deligne's construction of Grothendieck's six operations on the derived category of torsion sheaves over the \'etale site of a scheme for morphisms of finite type to a larger class of morphisms. This class includes…

In this paper we will obtain some further properties for specializations in a scheme. Using these results, we will take a picture for a scheme and a picture for a morphism of schemes. In particular, we will prove that every morphism of…

We develop the theory of mixed finite elements in terms of special inverse systems of complexes of differential forms, defined over cellular complexes. Inclusion of cells corresponds to pullback of forms. The theory covers for instance…

We give some results concerning the smoothness of the image of a real-analytic submanifold in complex space under the action of a finite holomorphic mapping. For instance, if the submanifold is not contained in a proper complex subvariety,…

We consider here the problem, which is quite classical in Algebraic geometry, of studying the secant varieties of a projective variety $X$. The case we concentrate on is when $X$ is a Veronese variety, a Grassmannian or a Segre variety. Not…

We give a partial "quasi-stratification" of the secant varieties of the order $d$ Veronese variety $X_{m,d}$ of $\mathbb {P}^m$. It covers the set $\sigma_t(X_{m,d})^{\dagger}$ of all points lying on the linear span of curvilinear…

From descent theory to higher geometry, the idea of gluing has been embedded in many elegant and powerful techniques, proving instrumental for the solution of many problems. In this paper, we introduce a framework that allows to link…

We study $T$-linear schemes, a class of objects that includes spherical and Schubert varieties. We provide a localization theorem for the equivariant Chow cohomology of these schemes that does not depend on resolution of singularities.…