Campedelli 曲面与 Burniat 曲面模空间的显式紧化

具有$p_g=0$的一般类型曲面的新旧示例

Old and new examples of surfaces of general type with $p_g=0$

研究了具有几何亏格$p_g=0$的一般型曲面，它可以表示为在具有Galois群$G=(\mathbb Z/q\mathbb Z)^k$的直线排列上分支的射影平面的Galois覆盖，其中$k\geq 2$和$q$是素数.经典的Godeaux曲面、Campedelli曲面、Burniat曲面和一种新的具有$K_X^2=6$和$(\mathbb Z/3\mathbb Z)^3\subset {Tors} (X)$的曲面$X$可以作为这样的覆盖而得到。证明了一般Campedelli型曲面的自同构群同构于$(\mathbb Z/2\mathbb Z)^3$ .描述了包含Burniat曲面的模空间的不可约分支。证明了具有$K_S^2=2$的Burniat曲面$S$具有挠群${Tors} (S)\simeq (\mathbb Z/2\mathbb Z)^3$（因此，它属于Campedelli曲面族），即，C. Peters“On certain examples of surfaces with $p_g=0$“in Nagoya Math. J. { \bf 66}（1977），and I. Dolgachev“Algebrakings surfaces with $q=p_g=0$“in { \it Algebrakings surfaces}，Liguori，Napoli（1977），an…

The compactifications of moduli spaces of Burniat surfaces with $2\leq K^{2}\leq5$

We describe compactifications of moduli spaces of Burniat surfaces with $2\leq K_{X}^{2}\leq5$ obtained by adding KSBA surfaces, i.e. slc surfaces $X$ with ample canonical class $K_{X}$.

次级与三级 Burniat 曲面模空间的显式 KSBA 紧化

Explicit KSBA compactifications of moduli spaces of secondary and tertiary Burniat surfaces

本文针对次数 $K^2=5$、$4$、$3$ 的次级与三级 Burniat 曲面模空间，给出通过添加典范类丰富的 slc 曲面所得的显式几何 KSBA 紧化。

KSBA空间上的Kappa类

Kappa classes on KSBA spaces

该研究在KSBA稳定簇及配对的模空间上定义了推广曲线模空间Miller-Morita-Mumford类的kappa类，并在含Burniat、Campedelli曲面的已知虚拟基本类存在情形中计算，还为Campedelli曲面求出了特定GIT商的Chow环。

Periods of an arrangement of six lines and Campedelli surfaces

We define a period map for classical Campedelli surfaces, using a covering trick as in the case of Enriques surfaces: the period map is shown to come from a family of Enriques surfaces, obtained as quotients of the Campedelli surface by an involution. The period map realises an isomorphism between a projective variety obtained by invariant theory, and the Baily-Borel compactification of an arithmetic quotient, in the same fashion as in the work of Matsumoto, Sasaki and Yoshida. The result is proved from scratch using traditional methods. As another consequence we determine properties of the mo…