Studies in Algebraic Geometry

Dolgachev 9970460这个建议的主要重点是研究K3型代数曲面的族，其总空间等于3维Calabi-Yau流形。 紧化在这种卡-丘流形上的弦理论及其对偶理论表明了自守形式理论与这类族的几何之间的一些有趣的关系。 我们建议将这个研究与已知的K3曲面的周期空间上自守形式的数学构造联系起来，研究的领域是代数几何。 这是数学的分支，研究与任意次数和任意变量的代数方程组有关的几何对象。 它起源于古希腊的圆锥曲线几何和勒内·笛卡尔的坐标方法。

Dolgachev9970460The main focus of this proposal is the study families of algebraic surfaces of type K3 with total space equal to a 3-dimensional Calabi-Yau manifold. The string theories compactified on such Calabi-Yau manifolds and their dual theories suggest some interesting relationships between the theory of automorphic forms and thegeometry of such families. We propose to relate this study to some known mathematical constructions of automorphic forms on the period spaces of K3 surfaces.The area of research in this proposal is algebraic geometry. This is the branch of mathematics dealing with geometric objects connected to systems of algebraic equations of arbitrary degree and in arbitrary number of variables. It has roots its in the ancient Greek geometry of conic sections and the method of coordinates of Rene Descartes.