On surfaces of class VII_0^+ with numerically anticanonical divisor

紧曲面上半正反正则除子补集的$\overline{\partial}$上同调

$\overline{\partial}$ cohomology of the complement of a semi-positive anticanonical divisor of a compact surface

本文研究具有半正曲率反正则线丛的紧复曲面上，其反正则除子补集的$\overline{\partial}$上同调群$H^1(M,\mathcal{O}_M)$的结构与性质。

Albanese morphism of log smooth klt compact Kähler manifold with nef log anticanonical divisor

Let $(X, ω)$ be an n-dimensional compact Kähler manifold. Let $D=\sum (1-β_j) Y_j=\sum (1-β_j) [s_j=0]$ a divisor with simple normal crossings with $β_j \in ]0,1[$ such that $-(K_X+D)$ is nef. We show that its Albanese map is submersion outside an analytic set of codimension larger than two with connected fibres.

Structure of projective varieties with nef anticanonical divisor: the case of log terminal singularities

In this article we study the structure of klt projective varieties with nef anticanonical divisor (and more generally, varieties of semi-Fano type), especially the canonical fibrations associated to them. We show that: 1. the Albanese map for such variety is a locally constant fibration (that is, an analytic fibre bundle with connected fibres that $X$ is equal to the product of the universal cover of the Albanese torus by the fibre of the Albanese map quotient by a diagonal action of the fundamenatl group of the Albanese torus); 2. if the smooth locus is simply connected, the MRC fibration of …

具有大典范或反典范除子的奇异簇的宫冈-丘不等式

The Miyaoka-Yau inequality for singular varieties with big canonical or anticanonical divisors

研究为具有大典范或反典范除子的奇异簇建立宫冈-丘不等式，定义非多极积，建立相关博戈莫洛夫-吉泽克型不等式，从而证明了特定射影klt簇的宫冈-丘不等式。

Logarithmic Moduli Spaces for Surfaces of Class VII

In this paper we describe logarithmic moduli spaces of pairs (S,D) consisting of minimal surfaces S of class VII with positive second Betti number b_2 together with reduced divisors D of b_2 rational curves. The special case of Enoki surfaces has already been considered by Dloussky and Kohler. We use normal forms for the action of the fundamental group of the complement of D and for the associated holomorphic contraction germ from (C^2,0) to (C^2,0).

Infinite bubbling in non-Kählerian geometry

In a holomorphic family $(X_b)_{b\in B}$ of non-Kählerian compact manifolds, the holomorphic curves representing a fixed 2-homology class do not form a proper family in general. The deep source of this fundamental difficulty in non-Kähler geometry is the {\it explosion of the area} phenomenon: the area of a curve $C_b\subset X_b$ in a fixed 2-homology class can diverge as $b\to b_0$. This phenomenon occurs frequently in the deformation theory of class VII surfaces. For instance it is well known that any minimal GSS surface $X_0$ is a degeneration of a 1-parameter family of simply blown up prim…