Zobrazeno 1 - 10
of 186
pro vyhledávání: '"van der Geer, Gerard"'
Autor:
van der Geer, Gerard, Yu, Xun
We give a bound on the number of weighted real forms of a complex variety with finite automorphism group, where the weight is the inverse of the number of automorphisms of the real form. We give another bound involving the Sylow 2-subgroup and as an
Externí odkaz:
http://arxiv.org/abs/2401.13284
We prove a formula for the cycle class of the supersingular locus in the Chow ring with rational coefficients of the moduli space of principally polarized abelian varieties in characteristic $p$. This formula determines this class as a monomial in th
Externí odkaz:
http://arxiv.org/abs/2307.14393
We construct vector-valued modular forms on moduli spaces of curves and abelian varieties using effective divisors in projectivized Hodge bundles over moduli of curves. Cycle relations tell us the weight of these modular forms. In particular we const
Externí odkaz:
http://arxiv.org/abs/2302.00329
Autor:
Cléry, Fabien, van der Geer, Gerard
We discuss two simple but useful observations that allow the construction of modular forms from given ones using invariant theory. The first one deals with elliptic modular forms and their derivatives, and generalizes the Rankin-Cohen bracket, while
Externí odkaz:
http://arxiv.org/abs/2211.05611
Autor:
van der Geer, Gerard
This is a survey paper dealing with moduli aspects of curves over finite fields. It discusses counting points of moduli spaces, relations with modular forms and stratifications on moduli spaces.
Comment: 29 pages. To appear in: Curves over finit
Comment: 29 pages. To appear in: Curves over finit
Externí odkaz:
http://arxiv.org/abs/2112.08704
Autor:
Cléry, Fabien, van der Geer, Gerard
We use the description of the Picard modular surface for discriminant $-3$ as a moduli space of curves of genus $3$ to generate all vector-valued Picard modular forms from bi-covariants for the action of ${GL}_2$ on the space of pairs of binary forms
Externí odkaz:
http://arxiv.org/abs/2110.00849
Autor:
van der Geer, Gerard
This is a survey based on the construction of Siegel modular forms of degree 2 and 3 using invariant theory in joint work with Fabien Cl\'ery and Carel Faber.
Comment: 19 pages; dedication added. To appear in: The Art of Doing Algebraic Geometry
Comment: 19 pages; dedication added. To appear in: The Art of Doing Algebraic Geometry
Externí odkaz:
http://arxiv.org/abs/2102.02245
Autor:
Bergström, Jonas, van der Geer, Gerard
We formulate a detailed conjectural Eichler-Shimura type formula for the cohomology of local systems on a Picard modular surface associated to the group of unitary similitudes $\mathrm{GU}(2,1,\mathbb{Q}(\sqrt{-3}))$. The formula is based on counting
Externí odkaz:
http://arxiv.org/abs/2012.07673
Autor:
Cléry, Fabien, van der Geer, Gerard
We describe the ring of modular forms of degree 2 in characteristic 2 using its relation with curves of genus 2.
Comment: 12 pages. Slight changes. To appear in IMRN
Comment: 12 pages. Slight changes. To appear in IMRN
Externí odkaz:
http://arxiv.org/abs/2003.00249
Publikováno v:
Tunisian J. Math. 3 (2021) 469-480
The moduli space of principally polarized abelian varieties $A_g$ of genus g is defined over the integers and admits a minimal compactification $A_g^*$, also defined over the integers. The Hodge bundle over $A_g$ has its Chern classes in the Chow rin
Externí odkaz:
http://arxiv.org/abs/1912.09687