Mathematical Sciences: Research Project in Geometry

这项研究涉及复杂代数几何的广泛领域，涉及三位研究者。本研究的统一主题是模空间的子变的几何。Carlson将研究Griffiths周期域的亚种，即Hodge结构的变化。克莱门斯将考虑一个固定品种的亚种和他们的阿贝尔-雅可比理论。托莱多将研究对称空间的子变种以及更一般的域的度量和泛函理论性质。这些主题是密切相关的，将产生许多联合性质的工作。本提案的主题是代数几何，研究几何对象作为多项式方程组的解的集合。这里的重点是研究它们的几何性质（而不是代数性质）。它仍然代表了代数，解析，当然还有几何思想的完美融合。这三个人作为一个强大的团队一起工作，产生了很大的兴趣。

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.