相关论文: Pluricanonical systems of projective 3-folds of ge…

This is a revised version of the second half of my paper math.AG/9909021. We prove that there exists a positive integer $\nu_{n}$ depending only on $n$ such that for every smooth projective $n$-fold of general type $X$ defined over complex…

This is a sequal paper to math.AG/9909021. By using the theory of AZD originated by the author, I prove that for every smooth projective $n$-fold $X$ of general type and every \[ m\geq \lceil\sum_{\ell =1}^{n}\sqrt[\ell]{2} \ell\rceil +1,…

We prove that there exists a positive integer $\nu_{n}$ depending only on $n$ such that for every smooth projective $n$-fold of general type $X$ defined over {\bf C}, $\mid mK_{X}\mid$ gives a birational rational map from $X$ into a…

Let $X$ be a complex smooth projective threefold of general type. Assume $q(X)>0$. We show that the $m$-canonical map of $X$ is birational for all $m\geq 5$.

We prove that for a smooth projective irregular $3$-fold $X$ with $K_X\equiv 0$ and a nef and big divisor $L$ on $X$, $|mL+P|$ gives a birational map for all $m\geq 3$ and all $P\in \text{Pic}^0(X)$. We also use the same method to deal with…

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 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.

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…

Any smooth projective curve embeds into $\mathbb{P}^3$. More generally, any curve embeds into a rationally connected variety of dimension at least three. We prove conversely that if every curve embeds in a threefold $X$, then $X$ is…

We prove that for every compact, connected, differentiable 3--manifold $M$ there is a compact complex manifold $X$ which can be obtained from projective 3--space by a sequence of smooth, real blow ups and downs such that $M$ is…

For smooth projective 3-folds of general type, we prove that the relative canonical stability $\mu_s(3)\leq 8$. This is induced from our improved result of Koll\'ar: the m-canonical map of a smooth projective 3-fold of general type is…

Let $X$ be a minimal projective 3-fold of general type. The pluricanonical section index $\delta(X)$ is defined to be the minimal integer $m$ so that $P_{m}(X)\geq 2$. According to Chen-Chen, one has either $1\leq \delta(X)\leq 15$ or…

We show that $|mK_X|$ defines a birational map and has no fixed part for some bounded positive integer $m$ for any $\frac{1}{2}$-lc surface $X$ such that $K_X$ is big and nef. For every positive integer $n\geq 3$, we construct a sequence of…

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…

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…

Let $V$ be a complex nonsingular projective 3-fold of general type with $\chi(\omega_V)\geq 0$ (resp. $>0$). We prove that the m-canonical map $\Phi_{|mK_V|}$ is birational onto its image for all $m\ge 14$ (resp. $\geq 8$). Known examples…

This paper aims to improve a theorem of Janos Kollar. For a given Complex projective threefold X of general type, suppose the plurigenus p_k(X)\ge 2, Kollar proved that the (11k+5)-canonical map is birational. Here we show that either the…

The authors give a complete classification of projective threefolds admitting a holomorphic normal projective connection. Moreover, they prove a general structure theorem on complex projective manifolds admitting a holomorphic normal…

For a minimal $3$-fold $X$ with $K_X\equiv 0$ and a nef and big Weil divisor $L$ on $X$, we investigate the birational geometry inspired by $L$. We prove that $|mL|$ and $|K_X+mL|$ give birational maps for all $m\geq 17$. The result remains…

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 $m\geq 73$…