形式的强度和切片秩一般相等
Strength and slice rank of forms are generically equal
摘要：
证明了特征为零的代数闭域上$d \geq 5$次齐次多项式的强度和片秩一般一致。为了证明这一点，我们建立了Catalisano，Geramita，Gimigliano，Harbourne，Migliore，Nagel和Shin关于可约齐次多项式簇的割线簇的维数的猜想。这些陈述在$2\leq d\leq 7$和$d=9$的程度上已经知道了。
英文摘要：
We prove that strength and slice rank of homogeneous polynomials of degree $d \geq 5$ over an algebraically closed field of characteristic zero coincide generically. To show this, we establish a conjecture of Catalisano, Geramita, Gimigliano, Harbourne, Migliore, Nagel and Shin concerning dimensions of secant varieties of the varieties of reducible homogeneous polynomials. These statements were already known in degrees $2\leq d\leq 7$ and $d=9$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
