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Quotients of E^n by a_(n+1) and Calabi-Yau manifolds

Paranjape, Kapil and Ramakrishnan, Dinakar (2005) Quotients of E^n by a_(n+1) and Calabi-Yau manifolds. In: Algebra and Number Theory: Proceedings of the Silver Jubilee Conference University of Hyderabad. Hindustan Book Agency , Gurgaon, pp. 90-98. ISBN 978-81-85931-57-9.

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We give a simple construction, for n ≥ 2, of an n-dimensional Calabi-Yau variety of Kummer type by studying the quotient Y of an n-fold self-product of an elliptic curve E by a natural action of the alternating group a_(n+1) (in n + 1 variables). The vanishing of H^m (Y, O_Y) for 0 < m < n follows from the lack of existence of (non-zero) fixed points in certain representations of a_(n+1). For n ≤ 3 we provide an explicit (crepant) resolution X in characteristics different from 2, 3. The key point is that Y can be realized as a double cover of ℙ^n branched along a hypersurface of degree 2(n + 1).

Item Type:Book Section
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Additional Information:© 2005 Hindustan Book Agency.
Subject Keywords:elliptic curve; Kummer surface; Calabi-Yau manifold; representations; alternating group; dual variety; crepant resolution
Classification Code:2000 Mathematics Subject Classification: 11G10; 14J28; 14J32; 20C30
Record Number:CaltechAUTHORS:20200221-155530980
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:101477
Deposited By: Tony Diaz
Deposited On:22 Feb 2020 19:28
Last Modified:16 Nov 2021 18:02

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