发帖
雷达卡
摘要翻译：
对于所有最小VII类曲面$S$和所有可能的Gauduchon度量$G$,我们显式地描述了在$C_1(E)=C_1(K)$和$C_2(E)=0$的秩2向量丛$E$上具有$\det E\cong K$的多稳定全纯结构$E$的模空间$M^{pst}_g(S,E)$。这些曲面$S$是非椭圆和非Kaehler复曲面，最近被完全分类。当$S$为半曲面或抛物型井上曲面时，$M^{pst}_g(S,E)$总是紧致的一维复圆盘。当$S$是一个Enoki曲面时，我们得到了一个具有有限个横向自交点的复圆盘，当$G$在Gauduchon度量空间中变化时，该自交点的数目变得任意大。$m^{pst}_g(S,E)$可以用PU(2)-瞬子的模空间来识别。上述类型的单丛的模空间导致了有趣的非Hausdorff奇异一维复空间的例子。
---
英文标题：
《Moduli Spaces of PU(2)-Instantons on Minimal Class VII Surfaces with
b_2=1》
---
作者：
Konrad Sch\"obel
---
最新提交年份：
2007
---
分类信息：
一级分类：Mathematics 数学
二级分类：Differential Geometry 微分几何
分类描述：Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis
复形，接触，黎曼，伪黎曼和Finsler几何，相对论，规范理论，整体分析
--
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
--
一级分类：Mathematics 数学
二级分类：Complex Variables 复变数
分类描述：Holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves
全纯函数，自守群作用与形式，伪凸性，复几何，解析空间，解析束
--
---
英文摘要：
We describe explicitly the moduli spaces $M^{pst}_g(S,E)$ of polystable holomorphic structures $E$ with $\det E\cong K$ on a rank 2 vector bundle $E$ with $c_1(E)=c_1(K)$ and $c_2(E)=0$ for all minimal class VII surfaces $S$ with $b_2(S)=1$ and with respect to all possible Gauduchon metrics $g$. These surfaces $S$ are non-elliptic and non-Kaehler complex surfaces and have recently been completely classified. When $S$ is a half or parabolic Inoue surface, $M^{pst}_g(S,E)$ is always a compact one-dimensional complex disc. When $S$ is an Enoki surface, one obtains a complex disc with finitely many transverse self-intersections whose number becomes arbitrarily large when $g$ varies in the space of Gauduchon metrics. $M^{pst}_g(S,E)$ can be identified with a moduli space of PU(2)-instantons. The moduli spaces of simple bundles of the above type leads to interesting examples of non-Hausdorff singular one-dimensional complex spaces.
---
PDF链接：
https://arxiv.org/pdf/0705.3349
京公网安备 11010802022788号
