论文标题
Frobenius推送线束的分解在奇妙的压缩上
Decomposition of Frobenius pushforwards of line bundles on wonderful compactifications
论文作者
论文摘要
de concini-procesi引入了称为奇妙的紧凑型品种，它们是半光滑的半圣母隔行组$ g $的投射压缩。我们研究了奇妙的紧凑型弗罗贝尼乌斯（Frobenius）的可逆滑轮，尤其是将其分解为本地免费的子店。我们提供了必要和足够的条件，使特定的线束成为另一线束的Frobenius Pushforward的直接汇总，该套件是根据$ \ widetilde {g} $的重量晶格（$ g $的通用封面）（与精美压实的Picard Group of the Greant compactification一起标识）的。在$ g = \ mathsf {psl} _n $的情况下，我们为满足足够条件的那些行捆绑包提供了多重性（作为直接汇总）的下限。我们还将线条捆绑包的Frobenius Pushforwards分解为直接的矢量子捆绑，其等级是由$ g $的重量晶格上的不变式确定的。我们研究了一个特定的块，该块将分解为直接捆绑包，并确定出现在该块中的线束。最后，我们提出了两种方法，以计算有理理性的Grothendieck集团和理性的Chow Group中出色的紧凑型线束的Frobenius Pushforward类。
De Concini-Procesi introduced varieties known as wonderful compactifications, which are smooth projective compactifications of semisimple adjoint groups $G$. We study the Frobenius pushforwards of invertible sheaves on the wonderful compactifications, and in particular its decomposition into locally free subsheaves. We give necessary and sufficient conditions for a specific line bundle to be a direct summand of the Frobenius pushforward of another line bundle, formulated in terms of the weight lattice of $\widetilde{G}$, the universal cover of $G$ (identified with the Picard group of the wonderful compactification). In the case of $G=\mathsf{PSL}_n$, we offer lower bounds on the multiplicities (as direct summands) for those line bundles satisfying the sufficient conditions. We also decompose Frobenius pushforwards of line bundles into a direct sum of vector subbundles, whose ranks are determined by invariants on the weight lattice of $G$. We study a particular block which decomposes as a direct sum of line bundles, and identify the line bundles which appear in this block. Finally, we present two approaches to compute the class of the Frobenius pushforward of line bundles on wonderful compactifications in the rational Grothendieck group and in the rational Chow group.
