相关论文: On pluricanonical maps for threefolds of general t…

This paper aims to study canonical pencils of higher dimensional projective varieties. It seems that the geometric genus of the general fibre for the derived fibration from the canonical pencil for a 3-fold of general type does not have an…

In this paper we study pluricanonical maps of minimal projective 3-folds of general type with geometric genus $1$, $2$ and $3$. We go in the direction pioneered by Enriques and Bombieri, and other authors, pinning down, for low projective…

We prove that for any smooth projective $3$-fold of general type with canonical volume greater than $12^6$, the image of its bicanonical map has dimension at least $2$. We also study pluricanonical maps of $3$-folds of general type with…

We prove that for all nonsingular projective 3-folds of general type with third plurigenus $P_3 \geq 2$, the pluricanonical map $\varphi_m$ is birational onto its image for all $m \geq 14$, which is optimal.

We classify minimal projective 3-folds of general type with $p_g = 2$ by studying the birationality of their 6-canonical maps.

In this paper we will prove that for a threefold of general type and large volume the second plurigenera is positive and the fifth canonical map is birational.

Let $V$ be a complex nonsingular projective 3-fold of general type. We prove $P_{12}(V):=\text{dim} H^0(V, 12K_V)>0$ and $P_{m_0}(V)>1$ for some positive integer $m_0\leq 24$. A direct consequence is the birationality of the pluricanonical…

We give some birationality criteria for $\phi_m$ (m=4,5,6,7) on general type 3-folds with $p_g\geq 2$ by means of an intensive classification.

We explicitly find lower bounds on the volume of threefolds and fourfolds of general type in order to have nonvanishing of pluricanonical systems and birationality of pluricanonical maps. In the case of threefolds of large volume, we also…

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…

We extend the known classification of threefolds of general type that are complete intersections to various classes of non-complete intersections, and find other classes of polarised varieties, including Calabi-Yau threefolds with canonical…

There are many examples of 3-folds of general type with $\chi(\mathcal {O})=1$ found by Iano-Fletcher and Reid about twenty years ago. Iano-Fletcher has ever proved $P_{12}(X)\ge 1$ and $P_{24}(X)\ge 2$ for all minimal 3-folds $X$ of…

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.

Let $V$ be a complex nonsingular projective 3-fold of general type. We shall give a detailed classification up to baskets of singularities on a minimal model of $V$. We show that the $m$-canonical map of $V$ is birational for all $m\geq 73$…

In this article we study the bicanonical map $\phi_2$ of quadruple Galois canonical covers X of surfaces of minimal degree. We show that $\phi_2$ has diverse behavior and exhibit most of the complexities that are possible for a bicanonical…

Nonsingular projective 3-folds $V$ of general type can be naturally classified into 18 families according to the {\it pluricanonical section index} $\delta(V):=\text{min}\{m|P_m\geq 2\}$ since $1\leq \delta(V)\leq 18$ due to our previous…

We consider $(1,1)$-surfaces, namely, minimal compact complex surfaces $S$ with $p_g (S) =K_S^2=1$: for these the bicanonical map is a covering of degree $4$ of the plane $\mathbb{P}^2$. And we answer a question posed by Meng Chen, whether…

We answer an open problem of the first author and Zhang (see Open Problem 6.4 (3) in Math. Z. 258 (2008), 565-585) and prove that, for any nonsingular projective $3$-fold of general type with the geometric genus greater than 201, the…

Let $X$ be a Gorenstein minimal projective $3$-fold with at worst locally factorial terminal singularities. Suppose that the canonical map is generically finite onto its image. C. Hacon showed that the canonical degree is universally…

We prove that the r-th pluricanonical maps of threefolds of general type have birationally bounded fibers if $r\geqslant 2$. Similarly, we prove that the r-th pluricanonical maps of fourfolds of general type have birationally bounded fibers…