Geodesic
The variety of polar simplices
Documenta mathematica, Tome 18 (2013), pp. 469-505
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A collection of n distinct hyperplanes Li​=li​=0⊂Pn−1, the (n−1)-dimensional projective space over an algebraically closed field of characteristic not equal to 2, is a polar simplex of a smooth quadric Qn−2=q=0, if each Li​ is the polar hyperplane of the point pi​=⋂j=i​Lj​, equivalently, if q=l12​+...+ln2​ for suitable choices of the linear forms li​. In this paper we study the closure VPS(Q,n)⊂Hilbn​(Pˇn−1) of the variety of sums of powers presenting Q from a global viewpoint: VPS(Q,n) is a smooth Fano variety of index 2 and Picard number 1 when n6, and VPS(Q,n) is singular when n≥6.
DOI : 10.4171/dm/406
Classification : 14J45
Mots-clés : quadric, Fano n-folds, polar simplex, syzygies 
@article{10_4171_dm_406,
     author = {Kristian Ranestad and Frank-Olaf Schreyer},
     title = {The variety of polar simplices},
     journal = {Documenta mathematica},
     pages = {469--505},
     year = {2013},
     volume = {18},
     doi = {10.4171/dm/406},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/406/}
}
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Kristian Ranestad; Frank-Olaf Schreyer. The variety of polar simplices. Documenta mathematica, Tome 18 (2013), pp. 469-505. doi: 10.4171/dm/406

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