On the height of Calabi-Yau varieties in positive characteristic

Autor: van der Geer, G., Katsura, T.

We study invariants of Calabi-Yau varieties in positive characteristic, especially the height of the Artin-Mazur formal group. We illustrate these results by Calabi-Yau varieties of Fermat and Kummer type.
Comment: Latex, 15 pages

Externí odkaz: http://arxiv.org/abs/math/0302023

Formal Brauer groups and the moduli of abelian surfaces

Autor: van der Geer, G., Katsura, T.

In this paper we consider the stratification on the moduli space of principally polarized abelian surfaces in characteristic $p>0$ defined by the height of the formal group associated to $H^2(X,O_X)$. We compute the cycle classes of the strata and co

Externí odkaz: http://arxiv.org/abs/math/9912169

Quadratic forms, generalized Hamming weights of codes and curves with many points

Autor: van der Geer, G., van der Vlugt, M.

We use the relations between quadrics, trace codes and algebraic curves to construct algebraic curves over finite fields with many points and to compute generalized Hamming weights of codes.
Comment: 14 pages, Plain TeX

Externí odkaz: http://arxiv.org/abs/alg-geom/9412011

Covariants of binary sextics and modular forms of degree 2 with character

Autor: Faber, C.F., van der Geer, G., Cléry, Fabien, Sub Fundamental Mathematics, Fundamental mathematics

Publikováno v: Mathematics of Computation, 88(319), 2423. American Mathematical Society
Mathematics of Computation, 88(319), 2423-2441. American Mathematical Society
Mathematics of Computation

We use covariants of binary sextics to describe the structure of modules of scalar-valued or vector-valued Siegel modular forms of degree 2 with character, over the ring of scalar-valued Siegel modular forms of even weight. For a modular form defined

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::39b5223972037ba1420beb0827a5a12c
https://hdl.handle.net/11245.1/45930df3-33d5-4616-a4c4-1febbb067384

Exploring modular forms and the cohomology of local systems on moduli spaces by counting points

Autor: van der Geer, G., Ji, L., Yau, S.-T.

Publikováno v: Uniformization, Riemann-Hilbert Correspondence, Calabi-Yau Manifolds & Picard-Fuchs Equations, 81-110
STARTPAGE=81;ENDPAGE=110;TITLE=Uniformization, Riemann-Hilbert Correspondence, Calabi-Yau Manifolds & Picard-Fuchs Equations

We report on a joint project in experimental mathematics with Jonas Bergstrom and Carel Faber where we obtain information about modular forms by counting curves over finite fields.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=narcis______::3cdb711dd4453a07bf946ee1e5869a67
https://dare.uva.nl/personal/pure/en/publications/exploring-modular-forms-and-the-cohomology-of-local-systems-on-moduli-spaces-by-counting-points(4c3ac9e6-be8c-467c-ab76-2007deb22295).html