论文标题
Chebyshev的潜力，Fubini-努力指标和Kähler指标空间的几何形状
Chebyshev potentials, Fubini--Study metrics, and geometry of the space of Kähler metrics
论文作者
论文摘要
威特·尼斯特罗姆（WittNyström）引入的投影品种的kähler潜力的Chebyshev潜力是Okounkov体内定义的凸功能。这是对Guillemin引入的曲折品种上的圆环kähler电位的合成电位的概括，这是Delzant Polytope上的凸函数。一个民间传说的猜想断言，当且仅当后一条曲线是mabuchi指标中的地球测量时，就在时间变量时，与曲线相关的Chebyshev电位曲线在时间变量中是线性的。在特殊的福利环境中，这在经典上是正确的，一般来说，维特·尼斯特罗姆（WittNyström）建立了足够的功能。本文的目的是反驳这一猜想。更普遍地，我们表征了fubini-distudy Geodesics，其猜想在投射空间上是正确的。证明涉及明确求解Monge-Ampère方程，描述了Fubini的子空间 - 研究指标并计算其Chebyshev潜力。
The Chebyshev potential of a Kähler potential on a projective variety, introduced by Witt Nyström, is a convex function defined on the Okounkov body. It is a generalization of the symplectic potential of a torus-invariant Kähler potential on a toric variety, introduced by Guillemin, that is a convex function on the Delzant polytope. A folklore conjecture asserts that a curve of Chebyshev potentials associated to a curve in the space of Kähler potentials is linear in the time variable if and only if the latter curve is a geodesic in the Mabuchi metric. This is classically true in the special toric setting, and in general Witt Nyström established the sufficiency. The goal of this article is to disprove this conjecture. More generally, we characterize the Fubini--Study geodesics for which the conjecture is true on projective space. The proof involves explicitly solving the Monge--Ampère equation describing geodesics on the subspace of Fubini--Study metrics and computing their Chebyshev potentials.
