论文标题
Fano品种分类中的计算和数据
Computation and data in the classification of Fano varieties
论文作者
论文摘要
Fano品种是代数品种的“原子片”，可以由多项式方程定义的形状。我们描述了计算和数据库方法在FANO品种的构建和分类中的作用，重点是三维Fano品种，其轻度奇异性称为Q-Fano三倍。 Q-Fano三倍的分类已经开放了几十年，但最近取得了重大进展。这些进步将计算代数几何形状和大规模数据分析与起源于理论物理学的新思想相结合。
Fano varieties are 'atomic pieces' of algebraic varieties, the shapes that can be defined by polynomial equations. We describe the role of computation and database methods in the construction and classification of Fano varieties, with an emphasis on three-dimensional Fano varieties with mild singularities called Q-Fano threefolds. The classification of Q-Fano threefolds has been open for several decades, but there has been significant recent progress. These advances combine computational algebraic geometry and large-scale data analysis with new ideas that originated in theoretical physics.
