Mathematical Sciences: Algebraic Geometry

数学科学：代数几何

• 批准号: 8703569
• 负责人: Henry Pinkham
• 金额: $ 41.57万
• 依托单位: Columbia University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-07-01 至 1990-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8703569&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Algebraic; Geometry

Professor Pinkham will study the m-regularity of smooth varieties in projective space via generic projection, and also the equations of canonical curves. Professor Friedman will continue to investigate Donaldson's new invariants for smooth 4- manifolds, especially elliptic surfaces and their blow-ups. The associate Principle Investigator Professor Morrison will study the slopes of effective divisors on the moduli space of stable curves, the stability of projective varieties via its state polytopes and the volume of simplices in spaces of constant curvature in terms of its dihedral angles along codimension two faces. The post doctoral assistant Dr. Cutkosky will study the birational geometry of threefolds concentrating on the analysis of the divisorial contraction of extremal rays. Finally the post doctoral assistant Dr. O'Grady will study the Kodaira dimension of the moduli space of polarized K3 surfaces of large degree. All of these topics are intermingled facets of the subject of algebraic geometry, the study of the geometric objects obtained as solution sets of systems of polynomial equations. The concentration in this proposal is on the geometric and topological aspects of these objects. This is an especially important area of modern mathematics with widespread applications. There is a rich mixture of young and mature investigators on this grant which will give the research an extra strength through their communication. There is a lot of promise in this research, much of which will surely be realized.

Pinkham教授将研究光滑的m-正则性 在射影空间中通过类属投影的变体，并且 正则曲线方程 弗里德曼教授将 继续研究唐纳森为平滑4-的新不变量 流形，特别是椭圆曲面及其爆破。 的 副首席研究员莫里森教授将研究 稳定模空间上有效因子的斜率 曲线，通过其状态的投射簇的稳定性 常值空间中的多面体与单形的体积 沿着余维二的二面角表示的曲率 脸上 博士后助理Cutkosky博士将研究 双有理几何的三倍集中在分析 极端射线分裂收缩的结果 最后，post 博士助理奥格雷迪博士将研究科代拉维度 的模空间的极化K3表面的大程度。 所有这些主题都是该主题的混合方面 代数几何学，研究几何对象 作为多项式方程组的解集获得。 本提案的重点是几何和 这些物体的拓扑结构。 这是一个特别 现代数学的重要领域， 应用. 有一个丰富的混合年轻和成熟 研究人员在这笔赠款，这将使研究额外的 通过他们的沟通。 有很多承诺 在这项研究中，其中大部分肯定会实现。