Results 1  10
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29
The exceptional cone and the Leech lattice
 Internat. Math. Res. Notices
, 1996
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Class invariants for quartic CM fields
, 2004
"... Abstract. One can define class invariants for a quartic primitive CM field K as special values of certain Siegel (or Hilbert) modular functions at CM points corresponding to K. Such constructions were given in [DSG] and [Lau]. We provide explicit bounds on the primes appearing in the denominators of ..."
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Cited by 11 (7 self)
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Abstract. One can define class invariants for a quartic primitive CM field K as special values of certain Siegel (or Hilbert) modular functions at CM points corresponding to K. Such constructions were given in [DSG] and [Lau]. We provide explicit bounds on the primes appearing in the denominators of these algebraic numbers. This allows us, in particular, to construct Sunits in certain abelian extensions of a reflex field of K, where S is effectively determined by K, and to bound the primes appearing in the denominators of the Igusa class polynomials arising in the construction of genus 2 curves with CM, as conjectured in [Lau]. 1.
Rational curves and points on K3 surfaces
 Amer. J. Math
"... Abstract. — We study the distribution of algebraic points on K3 surfaces. ..."
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Cited by 8 (4 self)
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Abstract. — We study the distribution of algebraic points on K3 surfaces.
Cubic surfaces and cubic threefolds, Jacobians and the intermediate Jacobians", Algebra, arithmetic, and geometry: in honor of
, 2009
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Computing Igusa class polynomials
, 2008
"... We give an algorithm that computes the genus two class polynomials of a primitive quartic CM field K, and we give a runtime bound and a proof of correctness of this algorithm. This is the first proof of correctness and the first runtime bound of any algorithm that computes these polynomials. Our alg ..."
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Cited by 6 (2 self)
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We give an algorithm that computes the genus two class polynomials of a primitive quartic CM field K, and we give a runtime bound and a proof of correctness of this algorithm. This is the first proof of correctness and the first runtime bound of any algorithm that computes these polynomials. Our algorithm uses complex analysis and runs in time e O( ∆ 7/2), where ∆ is the discriminant of K. 1
Twisted teichmüller curves
 Ph.D. thesis, Dissertation GoetheUniversität Frankfurt
, 2012
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On the Tannaka group attached to the Theta divisor of a generic principally polarized abelian variety, preprint available at arXiv:1309.3754
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NONHYPERELLIPTIC MODULAR JACOBIANS OF DIMENSION 3
, 2008
"... Abstract. We present a method to solve in an efficient way the problem of constructing the curves given by Torelli’s theorem in dimension 3 over the complex numbers: For an absolutely simple principally polarized abelian threefold A over C given by its period matrix Ω, compute a model of the curve o ..."
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Cited by 2 (0 self)
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Abstract. We present a method to solve in an efficient way the problem of constructing the curves given by Torelli’s theorem in dimension 3 over the complex numbers: For an absolutely simple principally polarized abelian threefold A over C given by its period matrix Ω, compute a model of the curve of genus three (unique up to isomorphism) whose Jacobian, equipped with its canonical polarization, is isomorphic to A as a principally polarized abelian variety. We use this method to describe the nonhyperelliptic modular Jacobians of dimension 3. We investigate all the nonhyperelliptic new modular Jacobians Jac(Cf) of dimension 3 which are isomorphic to Af,wheref∈Snew 2 (X0(N)), N ≤ 4000.
Infinite families of pairs of curves over Q with isomorphic Jacobians. Preprint arXiv
, 2003
"... Abstract. We present three families of pairs of geometrically nonisomorphic curves whose Jacobians are isomorphic to one another as unpolarized abelian varieties. Each family is parametrized by an open subset of P 1. The first family consists of pairs of genus2 curves whose equations are given by ..."
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Abstract. We present three families of pairs of geometrically nonisomorphic curves whose Jacobians are isomorphic to one another as unpolarized abelian varieties. Each family is parametrized by an open subset of P 1. The first family consists of pairs of genus2 curves whose equations are given by simple expressions in the parameter; the curves in this family have reducible Jacobians. The second family also consists of pairs of genus2 curves, but generically the curves in this family have absolutely simple Jacobians. The third family consists of pairs of genus3 curves, one member of each pair being a hyperelliptic curve and the other a plane quartic. Our constructions depend on earlier joint work with Franck Leprévost and Bjorn Poonen, and on Peter Bending’s explicit description of the curves of genus 2 whose Jacobians have real multiplication by Z [ √ 2]. 1.