稳定曲面的有效界

一般型曲面的典范模型称为典范曲面，各种有效界是其分类理论中的重要组成部分。稳定曲面是典范曲面的推广并包括其退化，从而被用来紧化典范曲面的模空间。由于所允许的奇点类型更多了，关于典范曲面的几个重要的有效界结果无法直接推广到稳定曲面上。为了更好地理解稳定曲面及其分类，我们拟从有效界的角度研究稳定曲面的地理问题、多典范映射及在模空间紧化中的具体应用。

The canonical models of surfaces of general type are called canonical surfaces and various kinds of boundedness are an important part of their classification theory. The notion of stable surfaces generalizes that of canonical surfaces and includes certain degenerations thereof. They are thus used to compactify the moduli spaces of canonical surfaces. Since more types of singularities are allowed, several important boundedness results for canonical surfaces do not generalize readily to stable surfaces. For a better understanding of stable surfaces and their classification we propose to study stable surfaces from the point of view of effective boundedness, concerning their geography, pluricanonical maps and concrete applications in compactifying moduli spaces.