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Moduli Spaces of Abelian Surfaces

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Part of the Lecture Notes in Mathematics book series (LNM,volume 2041)

Abstract

Let c \( \supset {C_F}\) be a fractional \( {C_F}\) -ideal. In this chapter we define c-polarized RM abelian surfaces and c-polarized CM abelian surfaces. The moduli space of all c-polarized RM abelian surfaces is a classical Hilbert modular surface, and the moduli space of all c-polarized CM abelian surfaces determines a codimension two cycle on the Hilbert modular surface. Useful references for Hilbert modular surfaces include [10], [14], [19], [46], [54], and [56].

Keywords

  • Modulus Space
  • Abelian Variety
  • Quaternion Algebra
  • Abelian Surface
  • Quadratic Space

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.

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Correspondence to Benjamin Howard .

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© 2012 Springer-Verlag Berlin Heidelberg

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Howard, B., Yang, T. (2012). Moduli Spaces of Abelian Surfaces. In: Intersections of Hirzebruch–Zagier Divisors and CM Cycles. Lecture Notes in Mathematics(), vol 2041. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23979-3_3

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