相关论文: Dually degenerate varieties and the generalization…

In this article we study the cohomological and homological (due to Jannsen) Hodge conjecture for singular varieties. The motivation for studying singular varieties comes from the fact that any smooth projective variety X is birational to a…

Consider a component of the Hilbert scheme whose general point corresponds to a degree d genus g smooth irreducible and nondegenerate curve in a projective variety X. We give lower bounds for the dimension of such a component when X is P^3,…

Let X be a nonsingular projective algebraic variety, and let S be a line bundle on X. Let A = (a_1,..., a_n) be a vector of integers. Consider a map f from a pointed curve (C,x_1,...,x_n) to X satisfying the following condition: the line…

We construct a double degenerate supersymmetry in one dimensional quantum mechanics. Here the energy levels satisfy the conditions $E_{0,1}^{((-)}=0$ and $E_{n,n+1}^{(+)}=E_{n+2,n+3}^{(-)}$.The corresponding SUSY Hamiltonians$(H^{(\pm)}$)…

Using the $\sharp$-minimal model program of uniruled varieties we show that for any pair $(X, \H)$ consisting of a reduced and irreducible variety $X$ of dimension $k \geq 3$ and a globally generated big line bundle $\H$ on $X$ with $d:=…

In this paper, by introducing the notion of "\textit{distributive constant}" of a family of hypersurfaces with respect to a projective variety, we prove a second main theorem in Nevanlinna theory for meromorphic mappings with arbitrary…

Motivated by DeVleming's work on moduli of surfaces in $\mathbb{P}^3$ and Chen-Hu-Jiang's work on moduli of threefolds with volume $2$ and geometric genus $4$, we study the deformation of pairs of $\mathbb{P}^3$ and hypersurfaces using the…

Let $X^n\subset C^{n+a}$ or $X^n\subset P^{n+a}$ be a patch of an analytic submanifold of an affine or projective space, let $x\in X$ be a general point, and let L^k be a linear space of dimension k osculating to order m at x. If m is large…

We study higher order determinantal varieties obtained by considering generic $m\times n$ ($m \le n$) matrices over rings of the form $F[t]/(t^k)$, and for some fixed $r$, setting the coefficients of powers of $t$ of all $r \times r$ minors…

An intriguing correspondence between four-qubit systems and simple singularity of type $D_4$ is established. We first consider an algebraic variety $X$ of separable states within the projective Hilbert space…

We investigate a scheme-theoretic variant of Whitney condition a. If X is a projec-tive variety over the field of complex numbers and Y $\subset$ X a subvariety, then X satisfies generically the scheme-theoretic Whitney condition a along Y…

Let $X$ be a submanifold of dimension $d\geq 2$ of the complex projective space $\mathbb P^n$. We prove results of the following type. i) If $X$ is irregular and $n=2d$ then the normal bundle $N_{X|\mathbb P^n}$ is indecomposable. ii) If…

Let $X\subset \P^N$ be a nondegenerate irreducible closed subvariety of dimension $n$ over the field of complex numbers and let $SX\subset\P^N$ be its secant variety. $X\subset\P^N$ is called `secant defective' if $\dim(SX)$ is strictly…

Let K be a finite extension of Q_p and X a smooth projective variety over K. We define the notion of totally degenerate reduction of such an X and the associated Chow complexes of the special fibre of a suitable regular proper model of X…

Consider a space X with the singular locus, Z=Sing(X), of positive dimension. Suppose both Z and X are locally complete intersections. The transversal type of X along Z is generically constant but at some points of Z it degenerates. We…

Let $\phi: X \to \mathbb P^n$ be a double cover branched along a smooth hypersurface of degree $2m, 2 \leq m \leq n-1$. We study the varieties of minimal rational tangents $\mathcal C_x \subset \mathbb P T_x(X)$ at a general point $x$ of…

We prove that any smooth complex projective variety with generic vanishing index bigger or equal than 2 has birational bicanonical map. Therefore, if X is a smooth complex projective variety X with maximal Albanese dimension and…

Let $X$ be a normal projective variety and $f:X\to X$ a non-isomorphic polarized endomorphism. We give two characterizations for $X$ to be a toric variety. First we show that if $X$ is $\mathbb{Q}$-factorial and $G$-almost homogeneous for…

Associated with an augmented differential graded algebra $R= R^{\geq 0}$ is a homotopy invariant ${\mathcal T}(R)$. This is a graded vector space, and if $H^0(R)$ is the ground field and $H^{>N}(R)= 0$ then dim$\, {\mathcal T}(R)= 1$ if and…

The purpose of this paper has twofold. The first is to establish a second main theorem with truncated counting functions for algebraically nondegenerate meromorphic mappings into an arbitrary projective variety intersecting a family of…