We study Gröbner degenerations of Schubert varieties inside flag varieties. We consider toric degenerations of flag varieties induced by matching fields and semi-standard Young tableaux. We describe an analogue of matching field ideals for Schubert varieties inside the flag variety and give a complete characterization of toric ideals among them. We use a combinatorial approach to standard monomial theory to show that block diagonal matching fields give rise to toric degenerations. Our methods and results use the combinatorics of permutations associated to Schubert varieties, matching fields and their corresponding tableaux.

中文翻译：

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标准单项式理论和Schubert品种从匹配场表获得的复曲面退化

我们研究了旗标品种内部舒伯特品种的Gröbner变性。我们考虑了由匹配场和半标准Young tableaux引起的标志品种的复曲面退化。我们在旗帜品种中描述了舒伯特品种的匹配场理想的类似物，并给出了其中复曲面理想的完整特征。我们使用标准单项式理论的组合方法来显示块对角线匹配场会导致复曲面退化。我们的方法和结果使用与Schubert品种，匹配字段及其对应表格相关的排列组合。