在无穷远处扩展Hodge范数
Extension of Hodge norms at infinity
AI总结：
本文研究如何将局部Hermitian对称空间的Satake-Baily-Borel紧化推广到任意周期映射，核心是证明在无穷远处的除数上holomorphic函数可扩展，通过构造伪凸复流形来实现Hodge范数的扩展。
摘要：
在Hodge理论中，将局部Hermitian对称空间的Satake-Baily-Borel紧化推广到任意周期映射是一个长期存在的问题。已构造出适当的拓扑SBB型完成，并将证明该构造代数性的任务减少到证明完成的纤维A的邻域X满足某些性质。除了一个之外，所有这些性质都已建立；剩下的问题是证明在某些无穷远处的除数上holomorphic函数可以延伸到X。此类延伸定理要求复流形X是伪凸的；即允许一个 plurisubharmonic 排除函数。X的邻域是分层的，各分层允许Hodge范数，可能用于在分层上产生 plurisubharmonic 函数。希望将这些范数延伸到X，以便用于构造X的所需 plurisubharmonic 排除函数。本文的目的在于证明存在一个函数，可以同时延伸所有在与纤维A非平凡相交的分层上 的Hodge范数。
英文摘要：
It is a long-standing problem in Hodge theory to generalize the Satake--Baily--Borel (SBB) compactification of a locally Hermitian symmetric space to arbitrary period maps. A proper topological SBB-type completion has been constructed, and the problem of showing that the construction is algebraic has been reduced to showing that the compact fibres A of the completion admit neighborhoods X satisfying certain properties. All but one of those properties has been established; the outstanding problem is to show that holomorphic functions on certain divisors "at infinity" extend to X. Extension theorems of this type require that the complex manifold X be pseudoconvex; that is, admit a plurisubharmonic exhaustion function. The neighborhood X is stratified, and the strata admit Hodge norms which are may be used to produce plurisubharmonic functions on the strata. One would like to extend these norms to X so that they may be used to construct the desired plurisubharmonic exhaustion of X. The purpose of this paper is show that there exists a function that simultaneously extends all the Hodge norms along the strata that intersect the fibre A nontrivially.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
