The generalized Plücker–Klein map

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The intersection of two quadrics is called a biquadric. If we mark a non-singular quadricin the pencil of quadrics through a given biquadric, then the given biquadric is called a marked biquadric. In the classical papers of Plücker and Klein, a Kummer surfacewas canonically associated with every three-dimensional marked biquadric (that is, witha quadratic line complex provided that the Plücker–Klein quadric is marked).In Reid's thesis, this correspondence was generalizedto odd-dimensional marked biquadrics of arbitrary dimension $\ge 3$. In this case,a Kummer variety of dimension $g$ corresponds to every biquadric of dimension $2g-1$.Reid only constructed the generalized Plücker–Klein correspondence. This map was notstudied later. The present paper is devoted to a partial solution of the problem of creatingthe corresponding theory.

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作者简介

Vyacheslav Krasnov

P.G. Demidov Yaroslavl State University

Email: vakras@yandex.ru
Doctor of physico-mathematical sciences, Associate professor

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