Contractions of subcurves of families of log curves

余数与亏格为一曲线的格森收缩

Residues and Gorenstein Contractions of Genus One Curves

本文研究了局部艺术代数环上亏格为一的节点曲线的余数及其在热带数据下的推广，进而构造出将子曲线收缩为格森亏格为一奇点的收缩映射。

超椭圆Gorenstein曲线与对数微分

Hyperelliptic Gorenstein curves and logarithmic differentials

本文提出一种局部且与基变换可交换的收缩对数超椭圆曲线子曲线的工具，并证明超椭圆多重尺度微分能决定底层节点曲线的Gorenstein收缩序列，为微分极限的更一般猜想提供了首个证据。

Families of D-minimal models and applications to 3-fold divisorial contractions

Let X/T be a one parameter family of canonical 3-folds and let D be a Weil divisor on it flat over T. We study the problem of when the D_t-minimal models of X_t form a family and we obtain conditions for this to happen. As an application of this we classify terminal divisorial contractions Y-->X that contract an irreducible divisor E onto a smooth curve C in the case when the general hyperplane section S of X through C is a D5 DuVal singularity.

Contraction centers in families of hyperkahler manifolds

We study the exceptional loci of birational (bimeromorphic) contractions of a hyperkähler manifold $M$. Such a contraction locus is the union of all minimal rational curves in a collection of cohomology classes which are orthogonal to a wall of the Kähler cone. Homology classes which can possibly be orthogonal to a wall of the Kähler cone of some deformation of $M$ are called MBM classes. We prove that all MBM classes of type (1,1) can be represented by rational curves, called MBM curves. All MBM curves can be contracted on an appropriate birational model of $M$, unless $b_2(M) \leq 5$. When $…

MBM loci in families of hyperkahler manifolds and centers of birational contractions

An MBM class on a hyperkahler manifold M is a second cohomology class such that its orthogonal complement in H^2(M) contains a maximal dimensional face of the boundary of the Kahler cone for some hyperkahler deformation of M. An MBM curve is a rational curve in an MBM class and such that its local deformation space has minimal possible dimension 2n-2, where 2n is the complex dimension of M. We study the MBM loci, defined as the subvarieties covered by deformations of an MBM curve within M. When M is projective, MBM loci are centers of birational contractions. For each MBM class z, we consider …

收缩族的代数方法

Algebraic approach to contraction families

本文提出了一种纯代数方法处理收缩群概型，并比较了其商概型与其他相关概型在对称和θ-稳定抛物子群情形下的群作用。