32 citations · 139 across the 27 of their papers we have counts for
32 papers
Tautological modular forms of level two and degree two
Fabien Cléry, Gerard van der Geer
We show how to use divisors on the projectivized Hodge bundle to construct special vector-valued modular forms and then apply invariant theory to construct all vector-valued Siegel…
On the number of real forms of a complex variety
Gerard van der Geer, Xun Yu
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…
The cycle class of the supersingular locus of principally polarized abelian varieties
Gerard van der Geer, Shushi Harashita
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 char…
Effective divisors on projectivized Hodge bundles and modular forms
Gerard van der Geer, Alexis Kouvidakis
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 relat…
Curves over finite fields and moduli spaces
Gerard van der Geer
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…
Generating Picard modular forms by means of invariant theory
Fabien Cléry, Gerard van der Geer
We use the description of the Picard modular surface for discriminant as a moduli space of curves of genus to generate all vector-valued Picard modular forms from bi-covar…
Siegel modular forms of degree two and three and invariant theory
Gerard van der Geer
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 Cléry and Carel Faber.
Lifting Chern classes by means of Ekedahl-Oort strata
Gerard van der Geer, Eduard Looijenga
The moduli space of principally polarized abelian varieties of genus g is defined over the integers and admits a minimal compactification , also defined over the integ…
Covariants of binary sextics and vector-valued Siegel modular forms of genus two
Fabien Cléry, Carel Faber, Gerard van der Geer
We extend Igusa's description of the relation between invariants of binary sextics and Siegel modular forms of degree two to a relation between covariants and vector-valued Siegel…
A stratification on the moduli of K3 surfaces in positive characteristic
Gerard van der Geer
We review the results on the cycle classes of the strata defined by the height and the Artin invariant on the moduli of K3 surfaces in positive characteristic obtained in joint wor…
Divisors on Hurwitz spaces: an appendix to 'The cycle classes of divisorial Maroni loci'
Gerard van der Geer, Alexis Kouvidakis
The Maroni stratification on the Hurwitz space of degree covers of genus has a stratum that is a divisor only if divides . Here we construct a stratification on th…
The cycle classes of divisorial Maroni loci
Gerard van der Geer, Alexis Kouvidakis
We determine the cycle classes of effective divisors in the compactified Hurwitz spaces of curves of genus g with a linear system of degree d that extend the Maroni divisors on the…
Counting curves over finite fields
Gerard van der Geer
This is a survey on recent results on counting of curves over finite fields. It reviews various results on the maximum number of points on a curve of genus g over a finite field of…
Constructing vector-valued Siegel modular forms from scalar-valued Siegel modular forms
Fabien Cléry, Gerard van der Geer
This paper gives a simple method for constructing vector-valued Siegel modular forms from scalar-valued ones. The method is efficient in producing the siblings of Delta, the smalle…
Siegel modular forms of genus 2 and level 2
Fabien Cléry, Gerard van der Geer, Samuel Grushevsky
We study vector-valued Siegel modular forms of genus 2 and level 2. We describe the structure of certain modules of vector-valued modular forms over rings of scalar-valued modular…
Relations between some invariants of algebraic varieties in positive characteristic
Gerard van der Geer, Toshiyuki Katsura
We discuss relations between certain invariants of varieties in positive characteristic, like the a-number and the height of the Artin-Mazur formal group. We calculate the a-number…
Generators for modules of vector-valued Picard modular forms
Fabien Cléry, Gerard van der Geer
We construct generators for modules of vector-valued Picard modular forms on a unitary group of type (2,1) over the Eisenstein integers. We also calculate eigenvalues of Hecke oper…
The cohomology of the moduli space of abelian varieties
Gerard van der Geer
This is a survey on various aspects of the cohomology of the moduli space of abelian varieties
Siegel modular forms of degree three and the cohomology of local systems
Jonas Bergström, Carel Faber, Gerard van der Geer
We give an explicit conjectural formula for the motivic Euler characteristic of an arbitrary symplectic local system on the moduli space A_3 of principally polarized abelian threef…
Cycle classes on the moduli of K3 surfaces in positive characteristic
Torsten Ekedahl, Gerard van der Geer
This paper provides explicit closed formulas in terms of tautological classes for the cycle classes of the height and Artin invariant strata in families of K3 surfaces. The proof i…
The class of a Hurwitz divisor on the moduli of curves of even genus
Gerard van der Geer, Alexis Kouvidakis
We calculate the cycle class of the Hurwitz divisor on the moduli space of stable curves of genus given by the degree covers of the projective line with simple r…
The rank-one limit of the Fourier-Mukai transform
Gerard van der Geer, Alexis Kouvidakis
We give a formula for the specialization of the Fourier-Mukai transform on a semi-abelian variety of torus rank 1.
Hunting for curves with many points
Gerard van der Geer
We construct curves with many points over finite fields using the class group
A note on Fano surfaces of nodal cubic threefolds
Gerard van der Geer, Alexis Kouvidakis
We study the Picard variety of the Fano surface of nodal and mildly cuspidal cubic threefolds in arbitrary characteristic by relating divisors on the Fano surface to divisors on th…