Related papers: Determinantal schemes and Buchsbaum-Rim sheaves

We introduce the fiber-full scheme which can be seen as the parameter space that generalizes the Hilbert and Quot schemes by controlling the entire cohomological data. The fiber-full scheme $\text{Fib}_{\mathcal{F}/X/S}^\mathbf{h}$ is a…

Let $X/\mathbb{F}_{q}$ be a smooth, geometrically connected, quasiprojective variety. Let $\mathcal{E}$ be a semisimple overconvergent $F$-isocrystal on $X$. Suppose that irreducible summands $\mathcal{E}_i$ of $\mathcal E$ have rank 2,…

We show that for any constructible sheaf F on a smooth algebraic variety X over a field of arbitrary characteristic its singular support SS(F) is equidimensional of dimension dim X. Here SS(F) is the minimal closed subset of the cotangent…

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…

To a smooth and proper morphism $\mathcal{X}\to U$ with quasicompact semiseparated target we associate a sheaf in the \'etale topology, which takes an affine $U$-scheme $V$ to the set of $V$-linear semiorthogonal decompositions (of fixed…

An analytic approach and description are presented for the moduli cotangent sheaf for suitable stable curve families including noded fibers. For sections of the square of the relative dualizing sheaf, the residue map at a node gives rise to…

Motivated by the work of Esnault-Hai, one has the notion of de Rham $K(\pi,1)$ schemes, defined as follows. Given a smooth proper geometrically connected scheme $X$ over a field $k$ of characteristic 0 and a base point $x \in X (k)$, one…

In this paper we study the incidence complex of an arbitrary morphism of locally free sheaves relative to an arbitrary quasi compact morphism of schemes. We prove it is a local complete intersection in the case when the sheaf morphism is…

An approximation scheme is a family of homogeneous subsets $(A_n)$ of a quasi-Banach space $X$, such that $A_1 \subsetneq A_2 \subsetneq ... \subsetneq X$, $A_n + A_n \subset A_{K(n)}$, and $\bar{\cup_n A_n} = X$. Continuing the line of…

Let W be a projective variety of dimension n+1, L a free line bundle on W, X in $H^0(L^d)$ a hypersurface of degree d which is generic among those given by sums of monomials from $L$, and let $f : Y \to X$ be a generically finite map from a…

The goal of this paper is to develop tools to study maximal families of Gorenstein quotients A of a polynomial ring R. We prove a very general Theorem on deformations of the homogeneous coordinate ring of a scheme Proj(A) which is defined…

Take a smooth, connected and non-degenerate projective curve $X\subset \mathbb {P}^r$, $r\ge 2b+2\ge 6$, defined over an algebraically closed field with characteristic $0$ and let $\sigma _b(X)$ be the $b$-secant variety of $X$. We prove…

In this paper we address a conjecture by Kleppe and Mir\'o-Roig stating that suitable twists by line bundles (on the smooth locus) of the exterior powers of the normal sheaf of a standard determinantal locus are arithmetically…

We consider the following conjecture: if X is a smooth projective variety over a field of characteristic zero, then there is a dense set of reductions X_s of X to positive characteristic such that the action of the Frobenius morphism on the…

A subscheme $X\subset \Bbb P^{n+3}$ of codimension $3$ is {\em Pfaffian} if it is the degeneracy locus of a skew-symmetric map $f:\cal{E}\spcheck(-t) @>>> \cal{E}$ with $\cal{E}$ a locally free sheaf of odd rank on $\Bbb P^{n+3}$. It is…

A primitive multiple scheme is a Cohen-Macaulay scheme $Y$ such that the associated reduced scheme $X=Y_{red}$ is smooth, irreducible, and that $Y$ can be locally embedded in a smooth variety of dimension $\dim(X)+1$. If $I_X$ is the ideal…

Let $X$ be any rational surface. We construct a tilting bundle $T$ on $X$. Moreover, we can choose $T$ in such way that its endomorphism algebra is quasi-hereditary. In particular, the bounded derived category of coherent sheaves on $X$ is…

The aim of this paper is to study the cohomology theory of monoid schemes in general and apply it to vector and line bundles. We will prove that over separated monoid schemes, any vector bundle is a coproduct of line bundles and then go on…

Consider a definably complete uniformly locally o-minimal expansion of the second kind of a densely linearly ordered abelian group. Let $f:X \rightarrow R^n$ be a definable map, where $X$ is a definable set and $R$ is the universe of the…

Let $S$ be a Dedekind scheme, $X$ a connected $S$-scheme locally of finite type and $x\in X(S)$ a section. The aim of the present paper is to establish the existence of the fundamental group scheme of $X$, when $X$ has reduced fibers or…