Algebraic Geometry Inspired by Physics

受物理学启发的代数几何

• 批准号: 0501000
• 负责人: Aaron Bertram
• 金额: --
• 依托单位: University of Utah
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-07-01 至 2008-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0501000&HistoricalAwards=false
• 关键词: Algebraic; Geometry; Inspired; Physics

Three projects in the theory of moduli in algebraic geometryare addressed in this proposal. The recent considerable influence ofstring theory on algebraic geometry has led to the introduction ofnew moduli spaces to study, new techniques for studying them, andinteresting ``quantum'' invariants defined in terms of them.This proposal is inspired by the physics, but remains firmly groundedin algebraic geometry.Moduli spaces are spaces that parametrize geometric objects.The first project deals with the spaces parametrizingholomorphic maps from the Riemann sphere to a complex projectivemanifold, and the ``Gromov-Witten'' invariants that can becomputed as integrals on such spaces. The second deals withthe spaces parametrizing holomorphic correspondences (i.e.Riemann surfaces lying over the Riemann sphere together witha holomorphic map to a complex projective manifold) as analternative source of Gromov-Witten invariants for Riemann surfacesof positive genus. The last project is an investigation ofmoduli spaces generalizing the spaces of holomorphicvector bundles on an algebraic surface.

本文提出了代数几何模理论中的三个方案。最近弦理论对代数几何的重大影响导致了新的模空间的引入，研究它们的新技术，以及根据它们定义的有趣的“量子”不变量。但在代数几何中仍然是牢固的。模空间是参数化几何对象的空间。第一个项目涉及从黎曼几何中参数化全纯映射的空间。球到一个复杂的projectivemanifold，和'' Gromov-Witten ''不变量，可以作为积分在这样的空间。第二部分讨论了全纯对应（即黎曼球面上的黎曼曲面和复射影流形上的全纯映射）作为正亏格的黎曼曲面的Gromov-Witten不变量的另一个来源的参数化空间。最后一个项目是对代数曲面上的全纯向量丛空间的模空间的研究。