New examples of hyperbolic octic surfaces in $\PP^3$

On the Geometry of the Moduli Space of Real Binary Octics

The moduli space of smooth real binary octics has five connected components. They parametrize the real binary octics whose defining equations have 0, 1, ..., 4 complex-conjugate pairs of roots respectively. We show that the GIT-stable completion of each of these five components admits the structure of an arithmetic real hyperbolic orbifold. The corresponding monodromy groups are, up to commensurability, discrete hyperbolic reflection groups, and their Vinberg diagrams are computed. We conclude with a simple proof that the moduli space of GIT-stable real binary octics itself cannot be a real hy…

Double coverings of octic arrangements with isolated singularities

In this paper we construct 206 examples of Calabi-Yau manifolds with different Euler numbers. All constructed examples are smooth models of double coverings of $P^3$ branched along an octic surface. We allow 11 types of (not necessary isolated) singularities in the branch locus. Thus we broaden the class of examples studied in math.AG/9902057. For every considered example we compute the Euler number and give a precise description of a resolution of singularities.

Geometry and Arithmetic of certain Double Octic Calabi-Yau Manifolds

We study Calabi-Yau manifolds constructed as double covers of ${\mathbb P}^3$ branched along an octic surface. We give a list of 85 examples corresponding to arrangements of eight planes defined over ${\mathbb Q}$. The Hodge numbers are computed for all examples. There are 7 rigid Calabi-Yau manifolds and 14 families with $h^{1,2}=1$. The modularity conjecture is verified for all the rigid examples.

八平面排列所定义的双八次卡拉比-约当三重流形的分类 II

Classification of double octic Calabi-Yau threefolds defined by an arrangement of eight planes II

本文通过研究八平面排列，完整分类了双八次卡拉比-约当三重流形，并揭示了其几何结构和模性新实例。

Examples of hyperbolic hypersurfaces of low degree in projective spaces

We construct families of hyperbolic hypersurfaces of degree $2n$ in the projective space $\mathbb{P}^n(\mathbb{C})$ for $3 \leq n \leq 6$.

两条平面曲线补集的不变双喷管与有效双曲性

Invariant two-jets and effective hyperbolicity for complements of two plane curves

该研究针对射影平面中两条光滑曲线补集，在特定次数条件下证明有效第二主定理，给出对应常数，结合陈希的轨迹得到补集的小林双曲性与双曲嵌入，通过构造不变双喷管微分等完成证明。