论文标题
关于混合空间的全球多键率理论
Global pluripotential theory on hybrid spaces
论文作者
论文摘要
令A为整体Banach环，而X/A为有限类型的投影方案，并具有半样品系列束L.我们在berkovich Analysitification x^An上L上的PSH（X，L）类PSH（X，L）定义了PSH（x，l），并在其上验证了各种基本属性。我们特别关注的是，A是复杂功率系列和X/A的混合环是一种光滑的品种，因此X^an是与穿刺磁盘上复杂品种的变性X相关的混合空间。然后，我们证明，当L足够时，零以对数增长的L上的任何plurisubharmonic度量标准，可以承认杂交空间X^hyb的规范性Plurisubharmonic扩展。我们还讨论了与连续的Plurisubharmonic杂种度量相关的Monge-Ampère措施家族的连续性。在x是规范两极化流形的变性的情况下，我们证明了规范的PSH扩展在XHYB上是连续的，并根据堕胎的规范模型（从MMP的意义上）明确描述了它。
Let A be an integral Banach ring, and X/A be a projective scheme of finite type, endowed with a semi-ample line bundle L. We define a class PSH(X,L) of plurisubharmonic metrics on L on the Berkovich analytification X^an and prove various basic properties thereof. We focus in particular on the case where A is a hybrid ring of complex power series and X/A is a smooth variety, so that X^an is the hybrid space associated to a degeneration X of complex varieties over the punctured disk. We then prove that when L is ample, any plurisubharmonic metric on L with logarithmic growth at zero admits a canonical plurisubharmonic extension to the hybrid space X^hyb . We also discuss the continuity of the family of Monge-Ampère measures associated to a continuous plurisubharmonic hybrid metric. In the case where X is a degeneration of canonically polarized manifolds, we prove that the canonical psh extension is continuous on Xhyb and describe it explicitly in terms of the canonical model (in the sense of MMP) of the degeneration.
