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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 $mgeq 73$ and that the canonical volume $text{Vol}(V)geq {1/2660}$. When $chi(mathcal{O}_V)leq 1$, our result is $text{Vol}(V)geq {1/420}$, which is optimal. Other effective results are also included in the paper.
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 $m_0leq 24$. A direct consequence is the birationality of the pluricanonical map $varphi_
Nonsingular projective 3-folds $V$ of general type can be naturally classified into 18 families according to the {it pluricanonical section index} $delta(V):=text{min}{m|P_mgeq 2}$ since $1leq delta(V)leq 18$ due to our previous series (I, II). Based
Let $V$ be a complex nonsingular projective 3-fold of general type. We prove $P_{12}(V)>0$ and $P_{24}(V)>1$ (which answers an open problem of J. Kollar and S. Mori). We also prove that the canonical volume has an universal lower bound $text{Vol}(V)
We prove that rationally connected Calabi--Yau 3-folds with kawamata log terminal (klt) singularities form a birationally bounded family, or more generally, rationally connected $3$-folds of $epsilon$-CY type form a birationally bounded family for $e
Let X be a smooth projective minimal 3-fold of general type. We prove the sharp inequality K^3_X >= (2 /3)(2p_g(X) - 5), an analogue of the classical Noether inequality for algebraic surfaces of general type