一般Hankel矩阵的坐标截面
Coordinate sections of generic Hankel matrices
摘要：
一个是特征为零的域$k$上的平方广义Hankel矩阵的坐标部分的退化，以及它的主要相关结构，如矩阵的行列式，由它的偏导数生成的理想，由这些导数定义的极映射，黑塞矩阵和矩阵的次极大子式的理想。证明了极映射对任何退化都是优势映射，而不是一般情况下的类球映射。考虑了矩阵的行列式$f$是否是具有（Segre）期望重数的Hessian的因子的问题，建立了$V(f)$对偶簇的期望下界.
英文摘要：
One deals with degenerations by coordinate sections of the square generic Hankel matrix over a field $k$ of characteristic zero, along with its main related structures, such as the determinant of the matrix, the ideal generated by its partial derivatives, the polar map defined by these derivatives, the Hessian matrix and the ideal of the submaximal minors of the matrix. It is proved that the polar map is dominant for any such degenerations, and not homaloidal in the generic case. The problem of whether the determinant $f$ of the matrix is a factor of the Hessian with the (Segre) expected multiplicity is considered, for which the expected lower bound of the dual variety of $V(f)$ is established.
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。
