论文标题
具有界强度的一组形式不关闭
The set of forms with bounded strength is not closed
论文作者
论文摘要
均匀多项式（或形式）的强度是表达其汇总的添加剂分解的最小长度，其汇总为还原形式。使用多项式函数，我们表明具有有界强度的形式集合并不总是扎成Zariski锁定的。更具体地说，如果地面磁场是代数关闭的，我们证明了具有强度$ \ leq3 $的四分之一的四分之一，对于大量变量而言，Zariski并不是Zariski封闭的。
The strength of a homogeneous polynomial (or form) is the smallest length of an additive decomposition expressing it whose summands are reducible forms. Using polynomial functors, we show that the set of forms with bounded strength is not always Zariski-closed. More specifically, if the ground field is algebraically closed, we prove that the set of quartics with strength $\leq3$ is not Zariski-closed for a large number of variables.
