关于维数为$$\ge 3$$的环状DM堆上的$$text\rm{H}-$$琐细线束

Pub Date : 2024-07-08 DOI:10.1007/s00229-024-01583-x

Lev Borisov, Chengxi Wang

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引用次数: 0

摘要

我们研究任意维度的光滑环形德利尼-蒙福堆栈 ${\mathbb {P}}_{\mathbf {\Sigma }}$ 上的线束。我们给出了一个充分条件，即当${\mathbb {P}}_{\mathbf {\Sigma }}$ 上的无限多线束具有琐碎同调时。在三维中，在 $\mathbf {\Sigma }$ 没有多于一对共线的技术假设下，这个充分条件也是必要条件。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

$On $$\textrm{H}-$$ trivial line bundles on toric DM stacks of dim $$\ge 3$$$

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On $$\textrm{H}-$$ trivial line bundles on toric DM stacks of dim $$\ge 3$$

We study line bundles on smooth toric Deligne-Mumford stacks ${\mathbb {P}}_{\mathbf {\Sigma }}$ of arbitrary dimension. We give a sufficient condition for when infinitely many line bundles on ${\mathbb {P}}_{\mathbf {\Sigma }}$ have trivial cohomology. In dimension three, this sufficient condition is also a necessary condition under the technical assumption that $\mathbf {\Sigma }$ has no more than one pair of collinear rays.

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