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Complete families of indecomposable non-simple abelian varieties
- Source :
- Mathematische Annalen. 382:255-283
- Publication Year :
- 2021
- Publisher :
- Springer Science and Business Media LLC, 2021.
-
Abstract
- Given a fixed product of non-isogenous abelian varieties at least one of which is general, we show how to construct complete families of indecomposable abelian varieties whose very general fiber is isogenous to the given product and whose connected monodromy group is a product of symplectic groups or is a unitary group. As a consequence, we show how to realize any product of symplectic groups of total rank $g$ as the connected monodromy group of a complete family of $g'$-dimensional abelian varieties for any $g'\ge g$. These methods also yield a construction of a new Kodaira fibration with fiber genus $4$.<br />22 pages
- Subjects :
- Pure mathematics
Group (mathematics)
General Mathematics
010102 general mathematics
Fibration
01 natural sciences
Mathematics - Algebraic Geometry
Mathematics::Algebraic Geometry
Monodromy
Unitary group
Product (mathematics)
0103 physical sciences
FOS: Mathematics
010307 mathematical physics
0101 mathematics
Abelian group
Indecomposable module
Algebraic Geometry (math.AG)
Mathematics::Symplectic Geometry
Mathematics
Symplectic geometry
Subjects
Details
- ISSN :
- 14321807 and 00255831
- Volume :
- 382
- Database :
- OpenAIRE
- Journal :
- Mathematische Annalen
- Accession number :
- edsair.doi.dedup.....5b665338a706287ebc4e26155315cc96