The degree of a projective subscheme has an upper bound in term of the codimension and the reduction number. If a projective variety has an almost maximal degree, that is, the degree equals to the upper bound minus one, then its Betti table has been described explicitly. We build on this work by showing that for most of such varieties, the defining ideals are componentwise linear and in particular the componentwise linearity is suitable for classifying the Betti tables of such varieties. As an application, we compute the Betti table of all varieties with almost maximal degree and componentwise linear resolution.

中文翻译：

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具有几乎最大度数的射影变体的分量线性

射影子方案的度在共维数和归约数方面有一个上限。如果一个射影变种有一个几乎最大的度数，即度数等于上界减一，那么它的 Betti 表已经被明确描述了。我们在这项工作的基础上证明，对于大多数此类变体，定义理想是分量线性的，特别是分量线性适用于对此类变体的 Betti 表进行分类。作为一个应用程序，我们以几乎最大程度和分量线性分辨率计算所有品种的 Betti 表。