Homaloidal determinants

详细信息    查看全文

• 作者：Maral Mostafazadehfard ; ¹ ; ^{maral@dmat.ufpe.br" class="auth_mail" title="E-mail the corresponding author} ; Aron Simis² ; ^{aron@dmat.ufpe.br" class="auth_mail" title="E-mail the corresponding author}
• 关键词：13B25 ; 13D02 ; 13H10 ; 13H15 ; 14E05 ; 14E07 ; 14J70 ; 14M05 ; 14M12
• 刊名：Journal of Algebra
• 出版年：2016
• 出版时间：15 March 2016
• 年：2016
• 卷：450
• 期：Complete
• 页码：59-101
• 全文大小：710 K

文摘

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 overall object of this work is the search for homaloidal polynomials that are the determinants of sufficiently structured square matrices. We focus particularly on the generic square Hankel matrix and other specializations or degenerations of the fully generic square matrix. In addition to studying the homaloidal nature of these determinants, one establishes several results on the ideal theoretic invariants of the respective Jacobian ideals, such as primary components, multiplicity, reductions and free resolutions.