半满性的一个刻画与相关曲线的收缩

4-dimensional symplectic contractions

Local symplectic contractions are resolutions of singularities which admit symplectic forms. Four dimensional symplectic contractions are (relative) Mori Dream Spaces. In particular, any two such resolutions of a given singularity are connected by a sequence of Mukai flops. We discuss the cone of movable divisors on such a resolution; its faces are determined by curves whose loci are divisors, we call them essential curves. The movable cone is divided into nef chambers which are related to different resolutions; this subdivision is determined by classes of 1-cycles. We also study schemes param…

次极大长度的除子型Mori收缩

Divisorial Mori contractions of submaximal length

本文改变极大长度假设，证明次极大长度的除子型Mori收缩的例外轨迹双有理等价于射影丛或二次曲面丛，拓展了Mori收缩相关刻画研究。

具有约化对数终端边界的Mori锥丛

Mori conic bundles with a reduced log terminal boundary

本文研究了相对维数为1的Mori压缩$f\colon X\to Z$的局部结构，并在此基础上进一步假设存在一个简化除子$S$，使得$K_X+S$是plt反样本的.

Shokurov's conjecture on conic bundles with canonical singularities

A conic bundle is a contraction $X\to Z$ between normal varieties of relative dimension $1$ such that $-K_X$ is relatively ample. We prove a conjecture of Shokurov which predicts that, if $X\to Z$ is a conic bundle such that $X$ has canonical singularities and $Z$ is $\mathbb{Q}$-Gorenstein, then $Z$ is always $\frac{1}{2}$-lc, and the multiplicities of the fibers over codimension $1$ points are bounded from above by $2$. Both values $\frac{1}{2}$ and $2$ are sharp. This is achieved by solving a more general conjecture of Shokurov on singularities of bases of lc-trivial fibrations of relative …

正特性下nef和大线丛的基点自由度

Basepoint freeness for nef and big line bundles in positive characteristic

本文给出了一个数值有效（nef）大线丛具有正特征的半满性的充要条件。一个应用是M_g上的泛稳定曲线的几何，特别是相对对偶层的正特征半满性。给出了一个例子，表明这一点和半振幅准则失败的特征零。第二个应用程序是森的程序的极小模型的3倍的积极特征，即存在的双有理极值收缩。