The variety of polar simplices

  • Kristian Ranestad

  • Frank-Olaf Schreyer

    053 Campus E2 4 Blindern D-66123 Saarbrücken NO-0316 Oslo Germany Norway
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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 .

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Kristian Ranestad, Frank-Olaf Schreyer, The variety of polar simplices. Doc. Math. 18 (2013), pp. 469–505

DOI 10.4171/DM/406