论文标题
舒伯特品种的有效分解定理
An effective decomposition theorem for Schubert varieties
论文作者
论文摘要
给定一个schubert variect $ \ mathcal {s} $包含在Grassmannian $ \ Mathbb {g} _ {k}（\ Mathbb {C}^{l}）$中，我们显示如何获取有关衍生的Pultived Pushforward $rπ_{*}的直接夏季信息的更多信息。 \ Mathbb {Q} _ {\ tilde {\ Mathcal {s}}} $由分解定理的应用给出，以适当的奇异性分辨率$π：\ tilde {\ tilde {\ Mathcal {s}}}}} \ rightArrow \ rightarrow \ rightArrow \ Mathcal \ Mathcal {s s} $。作为副产品，庞加莱多项式表达式与算法相同，该算法计算此类表达式中未知术语，并表明直接求和的实际数量恰好小于分解支持的数量。
Given a Schubert variety $\mathcal{S}$ contained in a Grassmannian $\mathbb{G}_{k}(\mathbb{C}^{l})$, we show how to obtain further information on the direct summands of the derived pushforward $R π_{*} \mathbb{Q}_{\tilde{\mathcal{S}}}$ given by the application of the decomposition theorem to a suitable resolution of singularities $π: \tilde{\mathcal{S}} \rightarrow \mathcal{S}$. As a by-product, Poincaré polynomial expressions are obtained along with an algorithm which computes the unknown terms in such expressions and which shows that the actual number of direct summands happens to be less than the number of supports of the decomposition.
