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Robin de Jong

  1. Second variation of Zhang's lambda-invariant on the moduli space of curves.

    Втр, 02/09/2010 - 16:01 — SomNambul
    Authors: Robin de Jong
    Subjects: Algebraic Geometry
    Abstract

    We study the second variation of the lambda-invariant introduced by Zhang on
    the complex moduli space of curves of genus g. As a result we prove that
    (8g+4)\lambda is equal, up to a constant, to the invariant \beta introduced
    some years ago by Hain and Reed. The \lambda-invariant measures the difference,
    at archimedean places, between the height of the canonical Gross-Schoen cycle
    and the Faltings stable height of a curve over a number field.

  2. Canonical height and logarithmic equidistribution on superelliptic curves.

    Пнд, 11/09/2009 - 16:01 — SomNambul
    Authors: Robin de Jong
    Subjects: Number Theory
    Abstract

    Let X be a smooth projective curve over a number field K given by an affine
    equation y^N=f(x) for some integer N>1 and for some monic and separable
    polynomial f(x) over K of degree larger than N and relative prime to N. We
    prove that the canonical height on the image of X in its jacobian can be
    written as a sum, over all places of K, of local integrals over X. We also
    prove that, except for possibly finitely many exceptions, these local integrals
    can be obtained by averaging over the n-division points of X.

Math-arch

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