The geometric and algebraic properties of smooth projective varieties with 1-regular structure sheaf are well understood, and the complete classification of these varieties is a classical result. The aim of this paper is to study the next case: smooth projective varieties with 2-regular structure sheaf. First, we give a classification of such varieties using adjunction mappings. Next, under suitable conditions, we study the syzygies of section rings of those varieties to understand the structure of the Betti tables, and show a sharp bound for Castelnuovo-Mumford regularity.

中文翻译：

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2-正则结构束光滑射影变种的分类与合合

具有1-正则结构层的光滑射影簇的几何和代数性质已被很好地理解，这些簇的完整分类是一个经典的结果。本文的目的是研究下一个案例：具有 2-正则结构层的光滑射影簇。首先，我们使用附属映射对此类品种进行分类。接下来，在合适的条件下，我们研究这些品种的节环的合子以了解 Betti 表的结构，并显示 Castelnuovo-Mumford 正则性的锐界。