无重数子簇的F-有理性质
F-rationality of multiplicity-free subvarieties
AI总结：
该研究在正特征域上证明了射影直线乘积中的无重数子簇具有F-有理奇点，强化了Brion关于此类子簇在特征0域上有有理奇点的结论。
AI中文摘要：
射影直线乘积中的无重数子簇，是指其周环类在标准基展开式中所有系数均为0或1的子簇。我们证明，在正特征域上，无重数子簇具有F-有理奇点。这强化了Brion的结果：无重数子簇是正规且Cohen–Macaulay的，且在特征0域上具有有理奇点。
英文摘要：
A multiplicity-free subvariety of a product of projective lines is a subvariety with the property that the expansion of its Chow class in the usual basis has all coefficients equal to 0 or 1. We show that, over a field of positive characteristic, a multiplicity-free subvariety has F-rational singularities. This strengthens Brion's result that multiplicity-free subvarieties are normal and Cohen--Macaulay, and that they have rational singularities over a field of characteristic 0.
