论文标题
局部环上过滤的多重性的凸度
Convexity of multiplicities of filtrations on local rings
论文作者
论文摘要
我们证明，局部环的过滤多样性满足各种凸特性。特别是，我们表明多重性是沿着测量学的凸。结果，我们证明了估值的体积是准经济估值简单上的日志凸，并给出了Xu和Zhuang定理的新证明，以实现归一化量最小化的唯一性。在另一个方向上，我们将REE的理想性定理推广到过滤中，并表征Minkowski过滤的不平等现象在轻度假设下是平等的。
We prove that the multiplicity of a filtration of a local ring satisfies various convexity properties. In particular, we show the multiplicity is convex along geodesics. As a consequence, we prove that the volume of a valuation is log convex on simplices of quasi-monomial valuations and give a new proof of a theorem of Xu and Zhuang on the uniqueness of normalized volume minimizers. In another direction, we generalize a theorem of Rees on multiplicities of ideals to filtrations and characterize when the Minkowski inequality for filtrations is an equality under mild assumptions.
