论文标题
一类Horikawa表面的KSBA模量中的单峰奇异性和边界除数
Unimodal singularities and boundary divisors in the KSBA moduli of a class of Horikawa surfaces
论文作者
论文摘要
具有$ k^2 = 1 $，$ p_g = 2 $的通用类型的平滑最小表面和$ q = 0 $构成了代数表面的地理学中的一个基本示例，而28维模量$ \ mathbf {m mathbf {m mathbf {m} $的最小型号通过模块化的$ \ mathiim}允许MATHIM} MTIM} MATIM} MMATIM} M. 程序。我们描述了这种紧凑型在参数降低的稳定表面中的八个新的不可还原边界分隔线。此外，我们研究了$ \ mathbf {m} $的GIT压实以及八个分化参数的退化表面的霍奇理论的关系。
Smooth minimal surfaces of general type with $K^2=1$, $p_g=2$, and $q=0$ constitute a fundamental example in the geography of algebraic surfaces, and the 28-dimensional moduli space $\mathbf{M}$ of their canonical models admits a modular compactification $\overline{\mathbf{M}}$ via the minimal model program. We describe eight new irreducible boundary divisors in such compactification parametrizing reducible stable surfaces. Additionally, we study the relation with the GIT compactification of $\mathbf{M}$ and the Hodge theory of the degenerate surfaces that the eight divisors parametrize.
