Mathematical Sciences: Research Project in Geometry

这项研究涉及复杂代数几何的广泛领域，涉及三名研究人员。研究的统一主题是模空间的子簇的几何。卡尔森将研究格里菲斯周期域的亚种，即霍奇结构的变化。克莱门斯将考虑固定变种的亚种和他们的Abel-Jacobi理论。托莱多将研究对称空间的子簇以及更一般的域的度量和函数论性质。这些主题密切相关，将产生许多共同性质的工作。这一建议的主题是代数几何，研究作为多项式方程组的解的集合而获得的几何对象。这里的重点是研究它们的几何(相对于它们的代数)性质。它仍然代表着代数思想、解析思想和几何思想的完美融合。这三个人作为一个强大的团队合作，产生了许多极具吸引力的作品。

This research is in the broad area of complex algebraic geometry and involves three investigators. The unifying theme of the research is the geometry of subvarieties of moduli spaces. Carlson will study subvarieties of the Griffiths period domains i.e. variations of Hodge structures. Clemens will consider subvarieties of a fixed variety and their Abel-Jacobi theory. Toledo will examine the metric and function-theoretic properties of subvarieties of symmetric spaces as well as of more general domains. These subjects are closely related and much work of a joint nature will result. The subject of this proposal is algebraic geometry, the study of the geometric objects obtained as the set of solutions of systems of polynomial equations. The emphasis here is the study of their geometric (as opposed to their algebraic) properties. It still represents a nice blend of algebraic, analytic and, of course, geometric ideas. The three individuals work together as a powerful team to produce much of great interest.