We prove the Conjecture of Catenese--Chen--Zhang: the inequality $K_X^3geq frac{4}{3}p_g(X)-frac{10}{3}$ holds for all projective Gorenstein minimal 3-folds $X$ of general type.
We show that 3-fold terminal flips and divisorial contractions to a curve may be factored by a sequence of weighted blow-ups, flops, blow-downs to a locally complete intersection curve in a smooth 3-fold or divisorial contractions to a point.
We show that if $X$ is a smooth complex projective variety with Kodaira dimension $0$ then the Kodaira dimension of a general fiber of its Albanese map is at most $h^0(Omega ^1 _X)$.
Let $X$ be a complex nonsingular projective 3-fold of general type. We show that there are positive constants $c$, $c$ and $m_1$ such that $chi (omega _X)geq -cVol (X)$ and $P_m(X)geq cm^3Vol (X)$ for all $mgeq m_1$.
