论文标题
Weil-Petersson潜力的连续性
Continuity of the Weil-Petersson potential
论文作者
论文摘要
Let $\mathcal{M}_{\rm KSB}$ (resp. $\mathcal{M}_{\rm KSB}'$) be the the moduli space of $n$-dimensional Kähler-Einstein manifolds (resp. varieties) $X$ with $K_X$ ample.我们证明，$ \ Mathcal {m} _ {\ rm ksb} $上的Weil-petersson指标唯一地扩展到投射品种$ \ MATHCAL {M} _ {\ rm KSB} $，作为封闭的正面当地电位，具有持续的本地电位。这概括了Wolpert的定理，该定理可以治疗$ n = 1 $的情况，并且还证实了伯曼 - 吉纳西亚的猜想。此外，我们得出了Kähler-Einstein电势的均值集量的均匀估计值
Let $\mathcal{M}_{\rm KSB}$ (resp. $\mathcal{M}_{\rm KSB}'$) be the the moduli space of $n$-dimensional Kähler-Einstein manifolds (resp. varieties) $X$ with $K_X$ ample. We prove that the Weil-Petersson metric on $\mathcal{M}_{\rm KSB}$ extends uniquely to the projective variety $\mathcal{M}_{\rm KSB}'$, as a closed positive current with continuous local potentials. This generalizes a theorem of Wolpert which treats the case $n=1$, and also confirms a conjecture of Berman-Guenancia. In addition, we derive uniform estimates for the volumes of sublevel sets of Kähler-Einstein potentials
