Two moduli spaces of abelian fourfolds with an automorphism of order five

Bert van Geemen; Matthias Schuett

Two moduli spaces of abelian fourfolds with an automorphism of order five

Algebraic Geometry 2012-07-13 v3

Authors: Bert van Geemen , Matthias Schuett

Abstract

We find explicit projective models of a compact Shimura curve and of a (non-compact) surface which are the moduli spaces of principally polarised abelian fourfolds with an automorphism of order five. The surface has a 24-nodal canonical model in IP^4 which is the complete intersection of two S_5-invariant cubics. It is dominated by a Hilbert modular surface and we give a modular interpretation for this. We also determine the L-series of these varieties as well as those of several modular covers of the Shimura curve.

Keywords

abelian fourfolds automorphism of order five moduli spaces Shimura curve Hilbert modular surface projective models L-series

Cite

@article{arxiv.1010.3897,
  title  = {Two moduli spaces of abelian fourfolds with an automorphism of order five},
  author = {Bert van Geemen and Matthias Schuett},
  journal= {arXiv preprint arXiv:1010.3897},
  year   = {2012}
}

Comments

27 pages; v3: 4.5 corrected

Two moduli spaces of abelian fourfolds with an automorphism of order five

Abstract

Keywords

Cite

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