Related papers: Polarized endomorphisms of normal projective three…

The main theorem of this paper is that, for a general pair $(A,X)$ of an (ample) Hypersurface $X$ in an Abelian Variety $A$, the canonical map $\Phi_X$ of $X$ is birational onto its image if the polarization given by $X$ is not principal…

Let $K$ be a local field with algebraically closed residue field and $X_K$ a torsor under an elliptic curve $J_K$ over $K$. Let $X$ be a proper minimal regular model of $X_K$ over the ring of integers of $K$ and $J$ the identity component…

Let $X$ be a smooth irreducible projective variety over a field $\mathbf{k}$ of dimension $d.$ Let $\tau: \mathbb{Q}_l\to \mathbb{C}$ be any field embedding. Let $f: X\to X$ be a surjective endomorphism. We show that for every…

We study the Cox realization of an affine variety, i.e., a canonical representation of a normal affine variety with finitely generated divisor class group as a quotient of a factorially graded affine variety by an action of the Neron-Severi…

Here we investigate the property of effectivity for adjoint divisors. Among others, we prove the following results: (i) A normal projective variety $X$ with at most canonical singularities is uniruled if and only if for each very ample…

In this article we study the structure of klt projective varieties with nef anticanonical divisor (and more generally, varieties of semi-Fano type), especially the canonical fibrations associated to them. We show that: 1. the Albanese map…

Let $f: X\to X$ be a surjective endomorphism of a projective variety of dimension $d$. The aim of this paper is to study the action of $f$ on the numerical group of divisors. For exmaple, I proved that $f$ is cohomologically hyperbolic if…

Assume that $X$ is an affine toric variety of characteristic $p > 0$. Let $\Delta$ be an effective toric $Q$-divisor such that $K_X+\Delta$ is $Q$-Cartier with index not divisible by $p$ and let $\phi_{\Delta}:F^e_* O_X \to O_X$ be the…

Let $X$ be a normal projective threefold with mild singularities, and $L_X$ a strictly nef $\mathbb{Q}$-divisor on $X$. First, we show the ampleness of $K_X+tL_X$ with sufficiently large $t$ if either the Kodaira dimension $\kappa(X)\neq 0$…

In this paper, we classify projective toric birational morphisms from Gorenstein toric 3-folds onto the 3-dimensional affine space with relatively ample anti-canonical divisors.

Let $X$ be a $\mathbb{Q}$-factorial klt projective variety admitting an int-amplified endomorphism $f$, i.e., the modulus of any eigenvalue of $f^*|_{\text{NS}(X)}$ is greater than $1$. We prove Kawaguchi-Silverman conjecture for $f$ and…

A $\mathbf{Q}$-Cartier divisor $D$ on a projective variety $M$ is {\it almost nup}, if $(D , C) > 0$ for every very general curve $C$ on $M$. An algebraic variety $X$ is of {\it almost general type}, if there exists a projective variety $M$…

In this paper, we study the Albanese morphisms in positive characteristic. We prove that the Albanese morphism of a variety with nef anti-canonical divisor is an algebraic fiber space, under the assumption that the general fiber is…

It is proved by M. Paun (1997, 2017) that the fundamental group of a compact Kahler manifold X is almost Abelian if the anti-canonical bundle -KX is nef. In this paper, we apply the recent geometric analytic theory of Kahler spaces…

A good canonical projection of a surface $S$ of general type is a morphism to the 3-dimensional projective space P^3 given by 4 sections of the canonical line bundle. To such a projection one associates the direct image sheaf F of the…

We describe a general program for studying the dynamics of surjective endomorphisms of algebraic varieties that are amenable to techniques from the minimal model program. We obtain density results on the pre-periodic points of surjective…

Let $K$ be a number field, $X$ a smooth projective variety over $K$ and $f: X \to X$ a polarized endomorphism of degree $d \geq 2$. We prove an exponential lower bound on $[K(\Per_n):K]$, where $\Per_n$ is the set of $n$-periodic points,…

We prove that the canonical ring of a canonical variety in the sense of de Fernex and Hacon is finitely generated. We prove that canonical varieties are klt if and only if R(-K_X) is finitely generated. We introduce a notion of nefness for…

Let $F$ be a torsionfree semistable coherent sheaf on a polarized normal projective variety. We prove that $F$ has a unique maximal locally free subsheaf $V$ such that $F/V$ is torsionfree and $V$ admits a filtration of subbundles for which…

Following the work of Totaro and Pereira, we study sufficient conditions under which collections of pairwise-disjoint divisors on a variety over an algebraically closed field are contained in the fibers of a morphism to a curve. We prove…