短旗簇的热带化与退化及其纤维
Tropicalization and degeneration of short flag varieties and their fibers
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中文总结 AI 辅助
本文研究线性退化短旗簇的热带化，利用拟阵方法证明其纤维在温和假设下为线性空间，从而给出其热带化的完整组合描述。
中文摘要 AI 辅助
参数化线性空间（旗）的格拉斯曼簇与旗簇的热带化已被深入研究，并揭示了丰富的组合结构。旗簇的线性退化提供了在格拉斯曼簇乘积与旗簇之间插值的方法。这些对象的热带版本最近已被引入，但其组合描述与计算仍具挑战性。我们考虑一个允许使用拟阵方法的特例，即参数化线性空间元组（其中一者的投影包含于另一者）的线性退化短旗簇。在温和假设下，其纤维本身是线性空间，这使得我们能够对其热带化进行全面组合描述，并由此对线性退化短旗簇的热带化进行全面组合描述。
英文摘要
Tropicalizations of Grassmannians resp. flag varieties parametrizing (flags of) linear spaces have been studied intensely and reveal rich combinatorial structure. Linear degenerations of flag varieties provide ways of interpolating between products of Grassmannians and flag varieties. Tropical versions of these have been introduced recently, but their combinatorial description and computation remains a challenge. We consider a particular case which allows the use of matroidal methods, namely linear degenerate short flag varieties parametrizing tuples of linear spaces such that a projection of one is contained in the other. Their fibers turn out to be linear spaces themselves under mild assumptions, which allows a comprehensive combinatorial description of their tropicalizations, and accordingly, of tropicalizations of linear degenerate short flag varieties.
发表机构
- Universität Tübingen（蒂宾根大学）
- RWTH Aachen（亚琛工业大学）
机构由 AI 辅助整理，请以论文原文为准。
