## Abelian Varieties: Proceedings of the International Conference held in Egloffstein, Germany, October 3-8, 1993The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications. |

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### Contents

1 | |

19 | |

25 | |

Compact complex manifolds bimeromorphic to tori | 55 |

Irrationality of the moduli spaces of polarized abelian surfaces | 63 |

Appendix to the paper Irrationality of the moduli spaces of polarized abelian surfaces | 83 |

Taufunctions and modules over the Virasoro algebra | 85 |

Some modular varieties related to P4 | 105 |

On a generalization of the NéronTate height on abelian varieties | 199 |

Refinements of the Tate conjecture for abelian varieties | 211 |

Complete subvarieties of moduli spaces | 225 |

AbelJacobi invariant and curves on generic abelian varieties | 237 |

The Schottky ideal | 251 |

Rational points on certain intersections of two quadrics | 273 |

On the Kodaira Dimension of moduli spaces of abelian varieties with nonprincipal polarizations | 293 |

Abelian surfaces with a polarization of type 14 | 303 |

New relations between the Fourier coefficients of modular forms of Nebentypus with applications to quaternary quadratic forms | 131 |

The fundamental group of some Siegel modular threefolds | 141 |

Spectral curves and PrymTjurin varieties I | 151 |

Symmetries of a moduli space of abelian surfaces | 323 |

List of contributors | 343 |

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### Common terms and phrases

abelian surfaces abelian varieties action algebra algebraic stack boundary component commutes compactiﬁcation conjugacy conjugate contained Corollary corresponding cusp form deﬁned deﬁnition degree denote dim(W dimension divisor elements of ﬁnite elliptic curves embedding equal equation equivalent ﬁber ﬁbre ﬁeld ﬁnd ﬁnite order ﬁrst ﬁxed points follows form of weight formula function Galois genus given Hence Hermitian highest weight Hilbert modular surfaces homomorphism implies induces intersection invariant involution irreducible isogeny isomorphic isotropy group Jacobi Kodaira dimension lattice Lemma line bundle linear Math matrix modular form moduli space morphism normal notation obtain orbit polynomials positive integer prime principal polarization projective Proof Proposition prove quadrics quotient rational representation resp respect ring satisﬁes Schottky semisimple Siegel modular forms singular spaces of abelian subgroup subvariety Suppose surjective symmetric tau-functions Theorem theta trivial vanishes vector Virasoro Virasoro algebra W-invariant zero