论文标题
确定性张量产品表面和移动Quadrics的方法
Determinantal tensor product surfaces and the method of moving quadrics
论文作者
论文摘要
张量产品表面$ \ mathscr {s} $是一个代数表面，定义为从$ \ mathbb {p}^1 \ times \ mathbb {p}^p}^1 $ to $ \ mathbb {p} $ to $ \ mathbb {p}^3 $ clotational map $ ϕ $的闭合。在假设$ ϕ $是通常的注入性的假设下，我们提供了$ \ Mathscr {s} $的新决定性表示形式，其基本点有限很多并且本地完整的交叉点。这些决定性表示形式是根据线性关系（Syzygies）的系数（Syzygies）和二次关系的二次关系构建的矩阵。我们的方法依赖于大卫·考克斯（David Cox）及其共同作者引入和研究的移动Quadrics方法的形式化和概括。
A tensor product surface $\mathscr{S}$ is an algebraic surface that is defined as the closure of the image of a rational map $ϕ$ from $\mathbb{P}^1\times \mathbb{P}^1$ to $\mathbb{P}^3$. We provide new determinantal representations of $\mathscr{S}$ under the assumptions that $ϕ$ is generically injective and its base points are finitely many and locally complete intersections. These determinantal representations are matrices that are built from the coefficients of linear relations (syzygies) and quadratic relations of the bihomogeneous polynomials defining $ϕ$. Our approach relies on a formalization and generalization of the method of moving quadrics introduced and studied by David Cox and his co-authors.
