齐次行列式
Homaloidal determinants
摘要：
域上的多项式环中的一个形式被称为类形的，如果它的极映射是Cremona映射，即，如果由形式的偏导数定义的有理映射具有逆有理映射。这项工作的目的是搜索的homaloidal多项式是充分结构化矩阵的决定因素。我们专注于通用catatalecticants，特别强调汉克尔矩阵。另一个重点是某些退化或专业化。除了研究这些决定因素的homaloidal性质，建立了几个结果的理想理论不变量的各自梯度理想，如主要成分，多重性，减少和自由分解。
英文摘要：
A form in a polynomial ring over a field is said to be homaloidal if its polar map is a Cremona map, i.e., if the rational map defined by the partial derivatives of the form has an inverse rational map. The object of this work is the search for homaloidal polynomials that are the determinants of sufficiently structured matrices. We focus on generic catatalecticants, with special emphasis on the Hankel matrix. An additional focus is on certain degenerations or specializations thereof. In addition to studying the homaloidal nature of these determinants, one establishes several results on the ideal theoretic invariants of the respective gradient ideals, such as primary components, multiplicity, reductions and free resolutions.
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