代数与解析：一项综述
Algebraic vs. analytic: a survey
浏览论文内容
中文总结 AI 辅助
该综述探讨复代数簇上解析映射是否存在代数代表的问题，关联霍奇型猜想，研究仿射簇全纯向量丛代数结构及映射同伦类代数代表等具体问题。
中文摘要 AI 辅助
给定一对复代数簇，我们可以提出问题：每个解析映射是否都有代数代表？当源簇和目标簇为非紧簇时，这类问题最受关注，此时问题与霍奇型猜想密切相关。我们从多个角度讨论这类问题的具体实例，包括：仿射簇上的哪些全纯向量丛具有代数结构，以及哪些同伦类的映射具有代数代表？
英文摘要
Given a pair of complex algebraic varieties, we can ask: does every analytic map admit an algebraic representative? Such questions are most interesting when the source and target are non-compact varieties, in which case the problems are closely linked with Hodge-type conjectures. Concrete avatars of this kind of problem, which we discuss from several points of view, include: which holomorphic vector bundles on an affine variety admit an algebraic structure, and which homotopy classes of maps admit algebraic representatives?
