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A note on varieties of weak CM-type.
- Source :
-
Journal of Geometry & Physics . Mar2024, Vol. 197, pN.PAG-N.PAG. 1p. - Publication Year :
- 2024
-
Abstract
- CM-type projective varieties X of complex dimension n are characterized by their CM-type rational Hodge structures on the cohomology groups. One may impose such a condition in a weakest form when the canonical bundle of X is trivial; the rational Hodge structure on the level- n subspace of H n (X ; Q) is required to be of CM-type. This brief note addresses the question whether this weak condition implies that the Hodge structure on the entire H ⁎ (X ; Q) is of CM-type. We study in particular abelian varieties when the dimension of the level- n subspace is two or four, and K3 × T 2. It turns out that the answer is affirmative. Moreover, such an abelian variety is always isogenous to a product of CM-type elliptic curves or abelian surfaces. This extends a result of Shioda and Mitani in 1974. [ABSTRACT FROM AUTHOR]
- Subjects :
- *ELLIPTIC curves
*ALGEBRAIC geometry
*COHOMOLOGY theory
*ABELIAN varieties
Subjects
Details
- Language :
- English
- ISSN :
- 03930440
- Volume :
- 197
- Database :
- Academic Search Index
- Journal :
- Journal of Geometry & Physics
- Publication Type :
- Academic Journal
- Accession number :
- 174974882
- Full Text :
- https://doi.org/10.1016/j.geomphys.2023.105084