The dual of the invariant quintic. (English) Zbl 0967.14033

Freitag, Eberhard; Hunt, Bruce

Exp. Math. 8, No. 2, 151-154 (1999).

From the paper: Given \(X\) as the zero-set of a polynomial, say, an explicit identification of \(X^\perp\) is difficult, except in very special cases. This article studies the case where \(X\) is a remarkable hyersurface of degree five (quintic), \(\text{I}5\subset \mathbb{P}^5\mathbb{C}\), the unique quintic that is invariant under the natural action of the Weyl group \(W(E_6)\) of the lattice \(E_6\). This quintic was investigated by B. Hunt in his book: “The geometry of some special arithmetic quotients” (1996; Zbl 0904.14025), chapter 6; and a certain amount of information about its dual was obtained. We identify explicitly the dual of this hypersurface I5.

MSC:

14N05	Projective techniques in algebraic geometry
14J35	\(4\)-folds
14Q10	Computational aspects of algebraic surfaces
14J70	Hypersurfaces and algebraic geometry

Keywords:

dual of quintic hypersurface

Citations:

Zbl 0904.14025

References:

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