The generalized Plücker–Klein map
- Авторлар: Krasnov V.A.1
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Мекемелер:
- P.G. Demidov Yaroslavl State University
- Шығарылым: Том 86, № 2 (2022)
- Беттер: 80-127
- Бөлім: Articles
- URL: https://ogarev-online.ru/1607-0046/article/view/142262
- DOI: https://doi.org/10.4213/im9073
- ID: 142262
Дәйексөз келтіру
Ашық рұқсат
Рұқсат берілді
Аннотация
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.
Негізгі сөздер
Толық мәтін
Авторлар туралы
Vyacheslav Krasnov
P.G. Demidov Yaroslavl State University
Email: vakras@yandex.ru
Doctor of physico-mathematical sciences, Associate professor
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