Towards a classification of rigid product quotient varieties of Kodaira dimension 0

In this paper the authors study quotients of the product of elliptic curves by a rigid diagonal action of a finite group G . It is shown that only for G = He ( 3 ) , Z 3 2 , and only for dimension ≥ 4 such an action can be free. A complete classification of the singular quotients in dimension 3 and...

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Bibliographic Details
Published inBollettino della Unione matematica italiana (2008) Vol. 15; no. 1-2; pp. 17 - 41
Main Authors Bauer, Ingrid, Gleissner, Christian
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.03.2022
Springer Nature B.V
Subjects
Classification
Curves
Mathematics
Mathematics and Statistics
Quotients
Hyperelliptic manifolds
14K99
Deformation theory
14J40
Rigid complex manifolds
Crystallographic groups
32G07
14B12
32G05
14J32
14L30
14J10
14B05
Quotient singularities
20H15
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Summary:In this paper the authors study quotients of the product of elliptic curves by a rigid diagonal action of a finite group G . It is shown that only for G = He ( 3 ) , Z 3 2 , and only for dimension ≥ 4 such an action can be free. A complete classification of the singular quotients in dimension 3 and the smooth quotients in dimension 4 is given. For the other finite groups a strong structure theorem for rigid quotients is proven.
ISSN:1972-6724
2198-2759
DOI:10.1007/s40574-021-00295-4