正特征单项式完全交集的非 Lefschetz 轨迹
The Non-Lefschetz Locus of Monomial Complete Intersections in Positive Characteristic
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中文总结 AI 辅助
本文完整刻画了正特征域上不满足弱 Lefschetz 性质的单项式完全交集的指数向量轨迹，并用出租车度量下正象限格球的平移显式描述该轨迹。
中文摘要 AI 辅助
在20世纪80年代，Stanley 和 J. Watanabe 证明了在特征为零的域上，每个单项式完全交集都具有强 Lefschetz 性质。确定正特征下哪些单项式完全交集具有弱 Lefschetz 性质一直是持续研究的课题。在本文中，我们给出了正特征域上对应于不满足弱 Lefschetz 性质的单项式完全交集的指数向量轨迹的完整描述。我们用出租车度量下正象限格球的平移来显式描述这一轨迹。
英文摘要
In the 1980s, Stanley and J. Watanabe proved that over a field of characteristic zero every monomial complete intersection has the strong Lefschetz property. Determining which monomial complete intersections in positive characteristic have the weak Lefschetz property has been the subject of ongoing research. In this paper, we give a complete description of the locus of exponent vectors corresponding to monomial complete intersections over a field of positive characteristic that fail the weak Lefschetz property. We describe this locus explicitly in terms of translates of positive-orthant lattice balls in the taxicab metric.
发表机构
- University of Nebraska–Lincoln（内布拉斯加大学林肯分校）
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