Fix integers g, d ≥ 1 and let A g,d denote the moduli stack associating to a scheme T the groupoid of pairs (A, λ), where A is an abelian scheme over T and λ : A → At is a polarization of degree d. Recall that this means that the kernel of λ is a finite flat group scheme over T of rank d2, and that fppf locally on T there exists an ample line bundle L on A such that the map
is equal to λ. In this case if f : A → T is the structural morphism then f*L is locally free of rank d on T and its formation commutes with arbitrary base change on T (see for example [36, I, §1] for a summary of basic properties of ample line bundles on abelian varieties).
Keywords
- Line Bundle
- Abelian Variety
- Group Scheme
- Ample Line Bundle
- Standard Construction
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
(2008). Moduli of Abelian Varieties with Higher Degree Polarizations. In: Compactifying Moduli Spaces for Abelian Varieties. Lecture Notes in Mathematics, vol 1958. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70519-2_6
Download citation
DOI: https://doi.org/10.1007/978-3-540-70519-2_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-70518-5
Online ISBN: 978-3-540-70519-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)
