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Prof.dr. G.B.M. van der Geer

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  • The rank-one limit of the Fourier-Mukai transform (2010)Open access

    Auteurs:Geer, van der G.; Kouvidakis, A.
    In:Documenta Mathematica, 15, 747 - 763. ISSN 14310635.

    Samenvatting:

    We give a formula for the specialization of the Fourier-Mukai transform on a semi-abelian variety of torus rank 1.

  • Cycle classes of the E-O stratification on the moduli of abelian varieties (2009)

    Auteurs:Ekedahl, T.; Geer, van der G.
    In:Algebra, arithmetic, and geometry: In honor of Yu. I. Manin: Volume I, 269, 567 - 636. Birkhäuser

    Samenvatting:

    We introduce a stratification on the space of symplectic flags on the de Rham bundle of the universal principally polarized abelian variety in positive characteristic. We study its geometric properties, such as irreducibility of the strata, and we calculate the cycle classes. When the characteristic

  • Siegel modular forms and their applications (2008)Open access

    Auteur:Geer, van der G.
    In:The 1-2-3 of modular forms: Lectures at a summer school in Nordfjordeid, Norway, 181 - 246. Springer

    Samenvatting:

    These are the lecture notes of the lectures on Siegel modular forms at the Nordfjordeid Summer School on Modular Forms and their Applications. We give a survey of Siegel modular forms and explain the joint work with Carel Faber on vector-valued Siegel modular forms of genus 2 and present evidence fo

  • Modular forms on Schiermonnikoog (2008)

    Auteurs:Edixhoven, B.; Geer, van der G.B.M.; Moonen, B.J.J.
    In:. Cambridge University Press

    Samenvatting:

    Modular forms are functions with an enormous amount of symmetry that play a central role in number theory, connecting it with analysis and geometry. They have played a prominent role in mathematics since the 19th century and their study continues to flourish today. Modular forms formed the inspirati

  • Andreotti-Mayer loci and the Schottky problem (2008)Open access

    Auteurs:Ciliberto, C.; Geer, van der G.B.M.
    In:Documenta Mathematica, 13, 453 - 504. ISSN 14310635.

    Samenvatting:

    We prove a lower bound for the codimension of the Andreotti-Mayer locus N-g,N-1 and show that the lower bound is reached only for the hyperelliptic locus in genus 4 and the Jacobian locus in genus 5. In relation with the intersection of the Andreotti-Mayer loci with the boundary of the moduli space

  • Siegel modular forms of genus 2 and level 2: Cohomological computations and conjectures (2008)

    Auteurs:Bergstrom, O.L.J.; Faber, C.F.; Geer, van der G.B.M.
    In:International Mathematics Research Notices, 2008, rnn100. ISSN 10737928.

  • The Euler characteristic of local systems on the moduli of curves and abelian varieties of genus three (2008)Open access

    Auteurs:Bergstrom, O.L.J.; Geer, van der G.B.M.
    In:Journal of Topology, 1(3), 651 - 662. ISSN 17538416.

    Samenvatting:

    We show how to calculate the Euler characteristic of a local system Vλ associated to an irreducible representation Vλ of the symplectic group of genus 3 on the moduli space M3 of curves of genus 3 and the moduli space A3 of principally polarised abelian varieties of dimension 3.

  • Cycle relations on Jacobian varieties. With an appendix by Don Zagier. (2007)Open access

    Auteurs:Geer, van der G.B.M.; Kouvidakis, A.
    In:Compositio Mathematica, 143(4), 900 - 908. ISSN 0010437x.

    Samenvatting:

    Abstract: By using the Grothendieck-Riemann-Roch theorem we derive cycle relations modulo algebraic equivalence in the Jacobian of a curve. The relations generalize the relations found by Colombo and van Geemen and are analogous to but simpler than the relations recently found by Herbaut. In an appe

  • Note on tautological classes of moduli of K3 surfaces (2005)

    Auteurs:Geer, van der G.B.M.; Katsura, T.
    In:Moscow Mathematical Journal, 5(4), 775 - 779. ISSN 16093321.

    Samenvatting:

    In this note, we prove some cycle class relations on moduli of K3 surfaces. Keywords: K3 surface, moduli space, tautological class.

  • Codes. (2005)Open access

    Auteur:Geer, van der G.B.M.
    In:Nieuwe Wiskrant, 25, 24 - 30. ISSN 09287167.

    Samenvatting:

    Wat zijn codes? Wellicht is het beter eerst te zeggen waarvoor codes gebruikt worden. Codes worden gebruikt om (digitale) data foutenvrij te transporteren. Dit betreft alle vormen van digitaal datatransport, variÄerend van satellietcommunicatie, internet, fax tot en met het lezen van een CD. In het

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