A collection of n distinct hyperplanes , the -dimensional projective space over an algebraically closed field of characteristic not equal to 2, is a polar simplex of a smooth quadric , if each is the polar hyperplane of the point , equivalently, if for suitable choices of the linear forms . In this paper we study the closure of the variety of sums of powers presenting from a global viewpoint: is a smooth Fano variety of index 2 and Picard number 1 when , and is singular when .
Cite this article
Kristian Ranestad, Frank-Olaf Schreyer, The variety of polar simplices. Doc. Math. 18 (2013), pp. 469–505DOI 10.4171/DM/406