arXiv subjects
Publications and source records attributed to Hsin-Ku Chen.
We prove that each divisorial contraction to a curve between terminal threefolds is a weighted blow-up under a suitable embedding. Moreover, we give a classification of the weighted blow-ups assuming that the curve is smooth.
Let X be a smooth threefold. We show that if $X_i\dashrightarrow X_{i+1}$ is a flip which appears in the $K_X$-MMP, then $c_1(X_i)^3-c_1(X_{i+1})^3$ is bounded by a constant depending only on $b_2(X)$.
We factorize three-dimensional terminal flops into a composition of divisorial contractions to points and blowing-up smooth curves.
We describe the resolution of singularities of a threefold which has minimal Picard number. We describe the relation between this minimal resolution and an arbitrary resolution of singularities.
We prove that for any smooth complex projective threefold of Kodaira dimension one, the $m$-th pluricanonical map is birational to the Iitaka fibration for every $m\geq5868$ and divisible by $12$.
We study Nash valuations and essential valuations of terminal threefolds of type $cA/r$. If $r=1$ or the given threefold is $\mathbb Q$-factorial, then all the Nash valuations and essential valuations can be completely described. We construct non-Gorenstein or non-$\mathbb Q$-factorial counter examples for the Nash problem.
Let $X$ be a smooth projective threefold. We prove that, among the process of minimal model program, the variance of the third Betti number can be bounded by some integer depends only on the Picard number of $X$.