论文标题
立方曲线和决定性表示的判别因子
Discriminants of cubic curves and determinantal representations
论文作者
论文摘要
平滑平面立方曲线的判别性可以写成theta函数的产物。这提供了代数和分析对象之间的重要联系。在本文中，我们采用了一种新的方法来通过使用确定性表示来获得这种经典结果。更确切地说，一个人可以代表非单明的立方形式，作为矩阵的矩阵的决定因素，其元素是线性形式。 theta的功能自然出现在该表示形式中，因此在立方体的歧视中出现。
The discriminant of a smooth plane cubic curve over the complex numbers can be written as a product of theta functions. This provides an important connection between algebraic and analytic objects. In this paper, we perform a new approach to obtain this classical result by using determinantal representations. More precisely, one can represent a non-singular cubic form as the determinant of a matrix whose elements are linear forms. Theta functions naturally appear in this representation and thus in the discriminant of the cubic.
