论文标题
Kähler-Einstein指标的家族
Families of singular Kähler-Einstein metrics
论文作者
论文摘要
精炼了Yau's和Kolodziej的技术，我们建立了非常精确的统一，对紧凑型Kähler歧管的退化复合复杂的Monge-ampère方程的先验估计值使我们能够控制解决方案的爆炸，因为同事类别和复杂结构都在变化。我们通过分析规范密度，建立统一的可整合性能，并开发家庭中多能理论的第一步，将这些估计值应用于具有扭曲的Kähler-Einstein指标的各种家族的研究。这提供了有关稳定品种模量空间的有趣信息，扩展了贝尔曼 - 古纳奇西亚和歌曲的作品，以及（log）calabi-yau品种上的单数ricci平面度量的行为，rong-ruan-zhang，gross-tosatti-zhang，gross-tosatti-zhang，collins-tosatti和tosatti和tosatti和tosatti-tosatti和tosatti-tosatti-tosatti-tosatti-tosatti-tosatti weekhang概括了作品。
Refining Yau's and Kolodziej's techniques, we establish very precise uniform a priori estimates for degenerate complex Monge-Ampère equations on compact Kähler manifolds, that allow us to control the blow up of the solutions as the cohomology class and the complex structure both vary. We apply these estimates to the study of various families of possibly singular Kähler varieties endowed with twisted Kähler-Einstein metrics, by analyzing the behavior of canonical densities, establishing uniform integrability properties, and developing the first steps of a pluripotential theory in families. This provides interesting information on the moduli space of stable varieties, extending works by Berman-Guenancia and Song, as well as on the behavior of singular Ricci flat metrics on (log) Calabi-Yau varieties, generalizing works by Rong-Ruan-Zhang, Gross-Tosatti-Zhang, Collins-Tosatti and Tosatti-Weinkove-Yang.
