Related papers: Canonical map of low codimensional subvarieties

Hyperbolic homogeneous polynomials with real coefficients, i.e., hyperbolic real projective hypersurfaces, and their determinantal representations, play a key role in the emerging field of convex algebraic geometry. In this paper we…

This paper proves that the 5-canonical map of a smooth minimal 3-fold is birational when the geometric genus is bigger than 2. A combination of the results in this paper and that of Ein-Lazarsfeld-Lee, the possible exceptional cases are…

Let X be the quasi-projective symplectic surface that is given by the total space of the invertible sheaf O(-2) over the projective line. Let Hilb X be the family of Hilbert schemes of points on X. We give and prove a closed formula…

Let $X\subset\mathbb{P}^{hn+h-1}$ be an irreducible and non-degenerate variety of dimension $n$. The Bronowski's conjecture predicts that $X$ is $h$-identifiable if and only if the general $(h-1)$-tangential projection…

The aim of this note is to use elementary methods to give a large class of examples of projective varieties $ Y \subseteq \mathbb{P}^d_k$ over a field $k$ with the property that $Y$ is not isomorphic to a hypersurface $H\subseteq…

Let $X,Y$ be two irreducible subvarieties of the projective space $\mathbb{P}^n$, and $d\geq 1$ an integer number. The main result of this paper is an algorithm to construct {\bf explicitly}, in terms of $d$ and the ideals defining $X$ and…

For $\epsilon$-lc Fano type varieties $X$ of dimension $d$ and a given finite set $\Gamma$, we show that there exists a positive integer $m_0$ which only depends on $\epsilon,d$ and $\Gamma$, such that both $|-mK_X-\sum_i\lceil mb_i\rceil…

For $E$ a presheaf of spectra on the category of smooth $k$-schemes satisfying Nisnevich excision, we prove that the canonical map from the algebraic singular complex of the theory $E$ with quasi-finite supports to the theory $E$ with…

Let $X$ be a smooth algebraic variety over $k$. We prove that any flat quasicoherent sheaf on $\operatorname{Ran}(X)$ canonically acquires a D-module structure. In addition, we prove that, if the geometric fiber $X_{\overline{k}}$ is…

Let $S$ be a nonsingular minimal complex projective surface of general type and the canonical map of $S$ is generically finite. Beauville showed that the geometric genus of the image of the canonical map is vanishing or equals the geometric…

Let $X$ be a complex projective variety. Suppose that the group of birational automorphisms of $X$ contains finite subgroups isomorphic to $(\mathbb{Z}/N\mathbb{Z})^r$ for $r$ fixed and $N$ arbitrarily large. We show that $r$ does not…

Classical Castelnuovo's Lemma shows that the number of linearly independent quadratic equations of a nondegenerate irreducible projective variety of codimension $c$ is at most ${{c+1} \choose {2}}$ and the equality is attained if and only…

We prove that in characteristic zero the multiplication of sections of dominant line bundles on a complete symmetric variety $X=\bar{G/H}$ is a surjective map. As a consequence the cone defined by a complete linear system over $X$, or over…

We consider the union of certain irreducible components of cohomological support loci of the canonical bundle, which we call standard. We prove a structure theorem about them and single out some particular cases, recovering and improving…

We show that if X is a nonsingular projective variety of general type over an algebraically closed field k of positive characteristic and X has maximal Albanese dimension and the Albanese map is separable, then |4K_X| induces a birational…

For a compact Riemann surface $X$ of any genus $g$, let $L$denote the line bundle $K_{X\times X}\otimes {\cal O}_{X\times X}(2\Delta)$ on $X\times X$, where $K_{X\times X}$ is the canonical bundle of $X\times X$ and $\Delta$ is the diagonal…

Given any finite quiver, we consider a complete flag of vector spaces over each vertex. Consider the unipotent invariant subalgebra of the coordinate ring of the filtered quiver representation subspace. We prove that the dimension of the…

Let $X$ be a projective minimal Gorenstein 3-fold of general type with canonical singularities. We prove that the 5-canonical map is birational onto its image.

In this paper we consider the problem of determining the Hilbert function of schemes X of the proiective space P^n which are the generic union of s lines and one m-multiple point. We completely solve this problem for any s and m when n > 3.…

We prove that the $5$-canonical map of every minimal projective $3$-fold $X$ with $K_X^3\geq 86$ is stably birational onto its image, which loosens previous requirements $K_X^3>4355^3$ and $K_X^3>12^3$ respectively given by Todorov and…