Recent publications

2026

1. Tautological modular forms of level 2 and degree 2

   Fabien Cléry and Gerard van der Geer

   arXiv:2605.13300

2024

1. On the number of real forms of a complex variety

   Gerard van der Geer and Xun Yu

   Épijournal de Géométrie Algébrique 9 (2025), art. 17

   arXiv:2401.13284

2023

1. The cycle class of the supersingular locus of principally polarized abelian varieties

   Gerard van der Geer and Shushi Harashita

   Selecta Mathematica (2025)

   arXiv:2307.14393published version

2. Effective divisors on projectivized Hodge bundles and modular forms

   Gerard van der Geer and Alexis Kouvidakis

   Mathematische Nachrichten

   arXiv:2302.00329published version

2022

1. Modular forms via invariant theory

   Fabien Cléry and Gerard van der Geer

   Research in Number Theory

   arXiv:2211.05611published version

2021

1. Curves over finite fields and moduli spaces

   Gerard van der Geer

   In: Curves over finite fields — past, present and future. Panoramas et Synthèses 60 (2023), 113–144, SMF

   arXiv:2112.08704published version

2. Generating Picard modular forms by means of invariant theory

   Fabien Cléry and Gerard van der Geer

   Pure and Applied Mathematics Quarterly 19 (2023)

   arXiv:2110.00849published version

3. Siegel modular forms of degree two and three and invariant theory

   Gerard van der Geer

   arXiv:2102.02245published version

2020

1. Picard modular forms and the cohomology of local systems on a Picard modular surface

   Jonas Bergström and Gerard van der Geer

   Commentarii Mathematici Helvetici 97 (2022), 305–381

   arXiv:2012.07673published version

2. Modular forms of degree two and curves of genus two in characteristic two

   Fabien Cléry and Gerard van der Geer

   IMRN

   arXiv:2003.00249published version

2019

1. Lifting Chern classes by means of Ekedahl–Oort strata

   Gerard van der Geer and Eduard Looijenga

   Tunisian Journal of Mathematics

   arXiv:1912.09687published version

2. The ring of modular forms of degree two in characteristic three

   Gerard van der Geer

   arXiv:1912.05161published version

3. Concomitants of ternary quartics and vector-valued Siegel and Teichmüller modular forms of genus three

   Fabien Cléry, Carel Faber and Gerard van der Geer

   Selecta Mathematica (2020)

   arXiv:1908.04248published version

2018

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

   Fabien Cléry, Carel Faber and Gerard van der Geer

   Mathematics of Computation

   arXiv:1803.05624published version

2017

1. On vector-valued Siegel modular forms of degree 2 and weight (j,2)

   Fabien Cléry and Gerard van der Geer, with two appendices by Gaëtan Chenevier

   Documenta Mathematica 23 (2018), 1129–1156

   arXiv:1709.01748published version

2016

1. Covariants of binary sextics and vector-valued Siegel modular forms of genus 2

   Fabien Cléry, Carel Faber and Gerard van der Geer

   Mathematische Annalen

   arXiv:1606.07014published version

2. Exploring modular forms and the cohomology of moduli spaces by counting points

   Gerard van der Geer

   Advanced Lectures in Mathematics 42, Int. Press 2018, 81–109. Expanded version of a talk at the Mittag-Leffler Institute

   arXiv:1604.02654published version

2015

1. A stratification on the moduli of K3 surfaces in positive characteristic

   Gerard van der Geer

   Arbeitstagung Bonn 2013: in memory of Friedrich Hirzebruch. Progress in Mathematics 319

   arXiv:1511.00345published version

2. Divisors on Hurwitz spaces — an appendix to ‘The cycle classes of divisorial Maroni loci’

   Gerard van der Geer and Alexis Kouvidakis

   Moscow Mathematical Journal

   arXiv:1510.07401published version

3. The cycle classes of divisorial Maroni loci

   Gerard van der Geer and Alexis Kouvidakis

   IMRN

   arXiv:1509.08598published version

2014

1. Constructing vector-valued Siegel modular forms from scalar-valued Siegel modular forms

   Fabien Cléry and Gerard van der Geer

   Pure and Applied Mathematics Quarterly 11 (2015), 21–47

   arXiv:1409.7176published version

2. Counting curves over finite fields

   Gerard van der Geer

   Finite Fields and their Applications

   arXiv:1409.6090published version

3. Corrigendum to: Andreotti–Mayer loci and the Schottky problem

   Ciro Ciliberto and Gerard van der Geer

   Documenta Mathematica 19 (2014), 993–1001

   Documenta Mathematica 19

2013

1. Modular forms of genus 2 and level 2

   Fabien Cléry, Gerard van der Geer and Samuel Grushevsky, with an appendix by Shigeru Mukai

   International Journal of Mathematics

   arXiv:1306.6018online version in IJM

2012

1. Relations between some invariants of algebraic varieties in positive characteristic

   Gerard van der Geer and Toshiyuki Katsura

   Rendiconti del Circolo Matematico di Palermo (2) 62 (2013), 111–125

   arXiv:1203.4093published version

2. Generators for modules of vector-valued Picard modular forms

   Fabien Cléry and Gerard van der Geer

   Nagoya Mathematical Journal (2013)

   arXiv:1202.0131published version

2011

1. The cohomology of the moduli space of abelian varieties

   Gerard van der Geer

   In: Handbook of Moduli (G. Farkas and I. Morrison, eds.)

   arXiv:1112.2294published version

2. Siegel modular forms of degree three and the cohomology of local systems

   Jonas Bergström, Carel Faber and Gerard van der Geer

   Selecta Mathematica (2013)

   arXiv:1108.3731published version

3. Rational correspondences between moduli spaces of curves defined by Hurwitz spaces

   Gerard van der Geer and Alexis Kouvidakis

   Journal of Pure and Applied Algebra 216 (2012), 876–893

   arXiv:1105.2383published version

4. Cycle classes on the moduli of K3 surfaces in positive characteristic

   Torsten Ekedahl and Gerard van der Geer

   Selecta Mathematica (2015)

   arXiv:1104.3024published version

2010

1. The Hodge bundle on Hurwitz spaces

   Gerard van der Geer and Alexis Kouvidakis

   Pure and Applied Mathematics Quarterly 7 (2011), 1297–1307. In memory of Eckart Viehweg

   arXiv:1010.3335published version

2. The class of a Hurwitz divisor on the moduli of curves of even genus

   Gerard van der Geer and Alexis Kouvidakis

   Asian Journal of Mathematics 16 (2012), 787–805

   arXiv:1005.0969published version

2009

1. The rank-one limit of the Fourier–Mukai transform

   Gerard van der Geer and Alexis Kouvidakis

   Documenta Mathematica 15 (2010), 747–763

   arXiv:0906.3793published version

2. A note on Fano surfaces of nodal cubic threefolds

   Gerard van der Geer and Alexis Kouvidakis

   Algebraic and arithmetic structures of moduli spaces (Sapporo 2007), 27–45. Advanced Studies in Pure Mathematics 58

   arXiv:0902.3877

3. Hunting for curves with many points

   Gerard van der Geer

   Coding and cryptology, 82–96. Lecture Notes in Computer Science 5557, Springer

   arXiv:0902.3882published version

2008

1. Siegel modular forms of genus 2 and level 2: cohomological computations and conjectures

   Jonas Bergström, Carel Faber and Gerard van der Geer

   IMRN 2008, art. ID rnn 100

   arXiv:0803.0917published version

2. Rank one Eisenstein cohomology of local systems on the moduli of abelian varieties

   Gerard van der Geer

   Science China Mathematics 54 (2011), 1621–1634

   arXiv:0802.2921published version

3. Modular forms

   Bas Edixhoven, Gerard van der Geer and Ben Moonen

   In: Modular Forms on Schiermonnikoog. Cambridge University Press 2008, 1–11

   pdf

2007

1. The Euler characteristic of local systems on the moduli of curves and abelian varieties of genus three

   Jonas Bergström and Gerard van der Geer

   Journal of Topology 1 (2008), 651–662

   arXiv:0705.0293published version

2. Andreotti–Mayer loci and the Schottky problem

   Ciro Ciliberto and Gerard van der Geer

   Documenta Mathematica 13 (2008), 453–504

   arXiv:math/0701353published versioncorrection

2006

1. Cycle relations on Jacobian varieties

   Gerard van der Geer and Alexis Kouvidakis

   Compositio Mathematica 143 (2007), 900–908

   arXiv:math/0608606published version

2. Siegel modular forms

   Gerard van der Geer

   In: The 1-2-3 of Modular Forms, Springer

   arXiv:math/0605346

2005

1. Note on tautological classes of moduli of K3 surfaces

   Gerard van der Geer and Toshiyuki Katsura

   Moscow Mathematical Journal 5 (2005), 775–779

   arXiv:math/0505211published version

2004

1. Cycle classes of the Ekedahl–Oort stratification on the moduli of abelian varieties

   Torsten Ekedahl and Gerard van der Geer

   Arithmetic, Algebra and Geometry — Manin Festschrift, Birkhäuser

   arXiv:math/0412272published version

2. The Euler characteristic of local systems on the moduli of hyperelliptic genus 3 curves

   Gilberto Bini and Gerard van der Geer

   Mathematische Annalen

   arXiv:math/0405427published version

3. Cycles representing the top Chern class of the Hodge bundle on the moduli space of abelian varieties

   Torsten Ekedahl and Gerard van der Geer

   Duke Mathematical Journal

   arXiv:math/0402274published version

2003

1. Complete subvarieties of moduli spaces and the Prym map

   Carel Faber and Gerard van der Geer

   Journal für die reine und angewandte Mathematik (Crelle)

   arXiv:math/0305334version in Crelle

2. Sur la cohomologie des systèmes locaux sur les espaces des modules des courbes de genre 2 et des surfaces abéliennes

   Carel Faber and Gerard van der Geer

   Comptes Rendus de l’Académie des Sciences, Paris

   arXiv:math/0305094part Ipart II

3. The order of the top Chern class of the Hodge bundle on the moduli space of abelian varieties

   Torsten Ekedahl and Gerard van der Geer

   Acta Mathematica

   arXiv:math/0302291published version

4. On the height of Calabi–Yau varieties in positive characteristic

   Gerard van der Geer and Toshiyuki Katsura

   Documenta Mathematica 2003

   arXiv:math/0302023published version

2002

1. An invariant for varieties in positive characteristic

   Gerard van der Geer and Toshiyuki Katsura

   Contemporary Mathematics

   arXiv:math/0201246published version

2001

1. The coset weight distribution of certain BCH codes and a family of curves

   Gerard van der Geer and Marcel van der Vlugt

   L’Enseignement Mathématique

   arXiv:math/0106089

2. An asymptotically good tower of curves over the field with eight elements

   Gerard van der Geer and Marcel van der Vlugt

   Bulletin of the London Mathematical Society

   arXiv:math/0102158version in Bull. LMS

2000

1. The top Chern class of the Hodge bundle on the moduli space of abelian varieties

   Torsten Ekedahl and Gerard van der Geer

   arXiv:math/0009104

2. Curves over finite fields and codes

   Gerard van der Geer

   Proceedings of the 3rd European Congress of Mathematics

   3ecm-talk, ps

3. Tables of curves with many points

   Gerard van der Geer and Marcel van der Vlugt

   Last update 17 February 2000. Replaces the Tables for numbers of points on curves over finite fields

   pdf

1999

1. Formal Brauer groups and moduli of abelian surfaces

   Gerard van der Geer and Toshiyuki Katsura

   arXiv:math/9912169

2. Moduli of abelian varieties and the singularities of the theta divisor

   Ciro Ciliberto and Gerard van der Geer

   arXiv:math/9911127published version

3. On a stratification of the moduli of K3 surfaces

   Gerard van der Geer and Toshiyuki Katsura

   Journal of the European Mathematical Society 2 (2000)

   arXiv:math/9910061published version

4. Kummer covers with many points

   Gerard van der Geer and Marcel van der Vlugt

   arXiv:math/9909037

5. Knopen

   Gerard van der Geer

   In: Vacantiecursus ‘Onbewezen Vermoedens’. CWI Syllabus (1999), 75–82. In het Nederlands

   knopen1.ps

6. Cycles on the moduli space of abelian varieties

   Gerard van der Geer

   In: Moduli of Curves and Abelian Varieties — the Dutch Intercity Seminar on Moduli, 65–89. Aspects of Mathematics, Vieweg 1999

   main.ps

1998

1. Effectivity of Arakelov divisors and the theta divisor of a number field

   Gerard van der Geer and René Schoof

   arXiv:math/9802121published version

2. Tables for numbers of points on curves over finite fields

   Gerard van der Geer and Marcel van der Vlugt

   Final update 19 March 1998. Superseded by Tables of curves with many points

   tables-Nqg-5.ps

1997

1. Generalizations of Deuring’s mass formula

   Gerard van der Geer

   Abstract of a talk given at San Feliu de Guíxols, 1997

   abstract, ps

2. Constructing curves with many points by solving linear equations

   Gerard van der Geer and Marcel van der Vlugt

   arXiv:alg-geom/9711010

3. Generalized Reed–Muller codes and curves with many points

   Gerard van der Geer and Marcel van der Vlugt

   arXiv:alg-geom/9710016

4. Knoten

   Gerard van der Geer

   General audience lecture

   brocker3.ps

5. The Chow ring of the moduli space of abelian threefolds

   Gerard van der Geer

   Journal of Algebraic Geometry 7 (1998)

   arXiv:alg-geom/9702009

1996

1. Generalized Hamming weights of codes and curves over finite fields with many points

   Gerard van der Geer and Marcel van der Vlugt

   Israel Mathematical Conference Proceedings 9 (1996), 417–432

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

   Gerard van der Geer and Marcel van der Vlugt

   Journal of Number Theory 59 (1996), 20–36

   arXiv:alg-geom/9412011

1995

1. On the existence of supersingular curves of given genus

   Gerard van der Geer and Marcel van der Vlugt

   Journal für die reine und angewandte Mathematik 458 (1995), 53–61

   arXiv:alg-geom/9404007published version

2. How to construct curves over finite fields with many points

   Gerard van der Geer and Marcel van der Vlugt

   arXiv:alg-geom/9511005