Recent publications

Title: Lifting Chern classes by means of Ekedahl-Oort strata
Authors: Gerard van der Geer, Eduard Looijenga
arXiv:1912.09687
Title: The ring of modular forms of degree two in characteristic three
Author: Gerard van der Geer
arXiv:1912.05161
Title: Concomitants of Ternary Quartics and Vector-valued Siegel and Teichmueller Modular Forms of Genus Three
Authors: Fabien Cléry, Carel Faber and Gerard van der Geer
arXiv:1908.04248
Title: Covariants of binary sextics and modular forms of degree 2 with character.
Authors: Fabien Cléry, Carel Faber and Gerard van der Geer
arXiv:1803.05624 and the published version
Title: On vector-valued Siegel modular forms of degree 2 and weight (j,2).
Authors: Fabien Cléry and Gerard van der Geer (with two appendices by Gaetan Chenevier)
arXiv:1709.01748 and the published version
Title: Covariants of binary sextics and vector-valued Siegel modular forms of genus 2
Authors: Fabien Cléry, Carel Faber and Gerard van der Geer
arXiv:1606.07014 and the published version
Comments: 19 pages. Published in Mathematische Annalen.
Title: Exploring modular forms and the cohomology of moduli spaces by counting points.
Author: Gerard van der Geer
arXiv:1604.02654 and the published version
In: Uniformization, Riemann-Hilbert correspondence, Calabi-Yau manifolds and Picard-Fuchs equations, 81--109,
Adv. Lect. Math. (ALM), 42, Int. Press, Somerville, MA, 2018.
Comments: 27 pages; expanded version of a talk at the Mittag-Leffler Institute.
Title:A stratification on the moduli of K3 surfaces in positive characteristic
Author: Gerard van der Geer
arXiv:1511.00345 and the published version
Comments: 16 pages; appears in: Arbeitstagung Bonn 2013: In Memory of Friedrich Hirzebruch. Progress in Math. 319.
Title: Divisors on Hurwitz spaces. An appendix to 'The cycle classes of divisorial Maroni loci'
Authors: Gerard van der Geer and Alexis Kouvidakis
arXiv:1510.07401 and the published version
Comments: 8 pages. Published in: Moscow Math. Journal.
Title: The cycle classes of divisorial Maroni loci
Authors: Gerard van der Geer and Alexis Kouvidakis
arXiv:1509.08598 and the published version
Comments: 34 pages. Published in IMRN.
Title: Constructing vector-valued Siegel modular forms from scalar-valued Siegel modular forms
Authors: Fabien Cléry and Gerard van der Geer
arXiv:1409.7176 and the published version
Comments: 21 pages. In: PAMQ 11 (2015), pp. 21-47.
Title: Counting curves over finite fields
Author: Gerard van der Geer
arXiv:1409.6090 and the published version
Comments: 25 pages; appears in Finite Fields and their Applications.
Corrigendum To: Andreotti--Mayer Loci and the Schottky Problem
Authors: Ciro Ciliberto and Gerard van der Geer
Documenta Mathematica 19 (2014) 993--1001
Title: Modular forms of genus 2 and level 2
Authors: Fabien Cléry, Gerard van der Geer and Samuel Grushevsky
Comments: 46 pages. With an appendix by Shigeru Mukai. Published in: International Journal of Mathematics.
math.AG/1306.6018 and online version in IJM
Title: Relations between some invariants of algebraic varieties in positive characteristic
Authors: Gerard van der Geer and Toshiyuki Katsura
Comments: 13 pages. Rend. Circ. Mat. Palermo (2) 62 (2013), no. 1, 111--125
math.AG/1203.4093 and the published version
Title: Generators for modules of vector-valued Picard modular forms
Authors: Fabien Cléry and Gerard van der Geer
Comments: 31 pages. Nagoya Math Journal 2013.
math.AG/1202.0131 and the published version
Title: The cohomology of the moduli space of abelian varieties
Author: Gerard van der Geer
Comments: 44 pages, Survey, to appear in Handbook of Moduli (G. Farkas and I. Morrison, eds.)
math.AG/1111.2294
Title: Siegel modular forms of degree three and the cohomology of local systems
Authors: Jonas Bergstroem, Carel Faber, Gerard van der Geer
Comments: 38 pages. Selecta Math 2013.
math.AG/1108.3731 published version
Title: Rational correspondences between moduli spaces of curves defined by Hurwitz spaces
Authors: Gerard van der Geer and Alexis Kouvidakis
Comments: 25 pages. J. Pure Appl. Algebra 216 (2012), no. 4, 876-893.
math.AG/1105.2383
Title: Cycle classes on the moduli of K3 surfaces in positive characteristic
Authors: Torsten Ekedahl and Gerard van der Geer
Comments: 32 pages; appears in Selecta Math 2015
math.AG/1104.3024 published version
Title: The Hodge class on Hurwitz spaces
Authors: Gerard van der Geer and Alexis Kouvidakis
Comments: 8 pages Pure Appl. Math. Q. 7 (2011), no. 4, Special Issue: In memory of Eckart Viehweg, 1297-1307.
math.AG/1010.3335
Title: The class of a Hurwitz divisor on the moduli of curves of even genus
Authors: Gerard van der Geer and Alexis Kouvidakis
Comments: 15 pages. Asian J. Math. 16 (2012), no. 4, 787-805.
math.AG/1005.0969
Title: The rank-one limit of the Fourier-Mukai transform
Authors: Gerard van der Geer and Alexis Kouvidakis
Comments: 15 pages. Doc. Math. 15 (2010), 747-763.
math.AG/0906.3793 the published version
Title: A note on Fano surfaces of nodal cubic threefolds
Authors: Gerard van der Geer and Alexis Kouvidakis
Comments: 14 pages. Algebraic and arithmetic structures of moduli spaces (Sapporo 2007), 27-45, Adv. Stud. Pure Math., 58, Math. Soc. Japan, Tokyo, 2010.
math.AG/0902.3877
Title: Hunting for curves with many points
Author: Gerard van der Geer
Comments: 13 pages. Coding and cryptology, 82-96, Lecture Notes in Comput. Sci., 5557, Springer, Berlin, 2009.
math.AG/0902.3882 and the published version
Title: Siegel modular forms of genus 2 and level 2: cohomological computations and conjectures
Authors: Jonas Bergstroem, Carel Faber and Gerard van der Geer
Comments: 15 pages, Latex, Int. Math. Res. Not. IMRN 2008, Art. ID rnn 100
math.AG/0803.0917 and the published version
Title: Rank one Eisenstein cohomology of local systems on the moduli of abelian varieties
Author: Gerard van der Geer
Comments: 17 pages, Latex, Sci. China Math. 54 (2011), no. 8, 1621-1634.
math.AG/0802.2921 The published version
Title: Modular Forms
Authors: Bas Edixhoven, Gerard van der Geer, Ben Moonen
Comments: Appears in: Modular Forms on Schiermonnikoog. Cambridge University Press. 2008, p. 1-11.
pdf-file
Title: The Euler characteristic of local systems on the moduli of curves and abelian varieties of genus three
Authors: Jonas Bergstroem and Gerard van der Geer
Comments: 15 pages, Latex, Journal of Topology 1, (3), 651-662 (2008)
math.AG/0705.0293 and the pdf file from Journal of Topology
Title: Andreotti-Mayer loci and the Schottky problem
Authors: Ciro Ciliberto and Gerard van der Geer
Comments: 46 pages, Latex, Documenta Math 13 (2008) 453--504
math.AG/0701353 and the pdf file from Documenta Mathematica
Title: Cycle relations on Jacobian varieties
Authors: Gerard van der Geer and Alexis Kouvidakis
Comments: 6 pages, Latex,
math.AG/0608606 and the pdf file from Compositio
Title: Siegel modular forms
Author: Gerard van der Geer
Comments: 54 pages, Latex,
math.AG/0605346 in: The 1-2-3 of Modular forms, Springer Verlag.
Title: Note on tautological classes of moduli of K3 surfaces
Authors: Gerard van der Geer and Toshiyuki Katsura
Comments: 5 pages, Latex, appeared in Moscow Math Journal 5 (2005), no. 4, 775--779
math.AG/0505211
Title: Cycle classes of the E-O stratification on the moduli of abelian varieties
Authors: Torsten Ekedahl and Gerard van der Geer
Comments: 60 pages, Latex. In: 'Arithmetic, Algebra and Geometry-- Manin- Festschrift', Birkhauser Verlag
math.AG/0412272 published version
Title: The Euler characteristic of local systems on the moduli of hyperelliptic genus 3 curves
Authors: Gilberto Bini and Gerard van der Geer
Comments: 12 pages, Latex,
math.AG/0405427 Appeared in Math. Annalen published version
Title: Cycles representing the top Chern class of the Hodge bundle on the moduli space of abelian varieties
Authors: Torsten Ekedahl and Gerard van der Geer
Comments: 10 pages, Latex,
math.AG/0402274 published version in Duke Math. Journal.
Title: Complete subvarieties of moduli spaces and the Prym map
Authors: Carel Faber, Gerard van der Geer
Comments: 19 pages, 1 figure, plain tex
math.AG/0305334 Appeared in Crelle
Title: Sur la cohomologie des syst'emes locaux sur les espaces des modules des courbes de genre 2 et des surfaces abe'liennes
Authors: C. Faber, G. van der Geer
Comments: 7 pages, Latex, appeared in C.R.Acad.Sci Paris
math.AG/0305094 Published version Part I Part II
Title: The order of the top Chern class of the Hodge bundle on the moduli space of abelian varieties
Authors: Torsten Ekedahl and Gerard van der Geer
Comments: 12 pages, Latex, These results improve the first half of math.AG/0009104. Appeared in Acta Mathematica
math.AG/0302291and published version
Title: On the height of Calabi-Yau varieties in positive characteristic
Authors: G. van der Geer, T. Katsura
Comments: 15 pages, Latex , appears in Documenta Math, 2003
math.AG/0302023 Appeared in Documenta
Title: An invariant for varieties in positive characteristic
Authors: G. van der Geer, T. Katsura
Comments: 11 pages, Latex
math.AG/0201246 Appeared in Contemp. Math.
Title: The coset weight distribution of certain BCH codes and a family of curves
Author(s): Gerard van der Geer and Marcel van der Vlugt
Comments: 15 pages, Plain Tex
math.AG/0106089 Appeared in Enseignement Math.
Title: An asymptotically good tower of curves over the field with eight elements.
Author(s): Gerard van der Geer and Marcel van der Vlugt
Comments: 12 pages, Plain Tex
math.AG/0102158 Appeared in Bull. London Math Soc.
Title: The top Chern class of the Hodge bundle on the moduli space of abelian varieties
Author(s): Torsten Ekedahl and Gerard van der Geer
Comments: 10 pages, Latex
math.AG/0009104
Curves over Finite Fields and Codes;
Author(s): G. van der Geer
Comments: 15 pages, ps-file ; paper in the 3ECM proceedings
3ecm-talk
Title: Formal Brauer groups and moduli of abelian surfaces
Author(s): G. van der Geer and T. Katsura
Comments: 27 pages, Latex
math.AG/9912169
Title: Moduli of Abelian Varietes and the Singularities of the Theta Divisor
Author(s): Ciro Ciliberto and G. van der Geer
Comments: 17 pages, Plain Tex
math.AG/9911127
Title: On as Stratification of the Moduli of K3 Surfaces
Author(s): G. van der Geer and T. Katsura
Comments: 28 pages, Plain Tex. J. Eur. Math. Soc 2 (2000),
math.AG/9910061
Title: Kummer covers with Many Points
Author(s): Gerard van der Geer and Marcel van der Vlugt
Comments: 13 pages, Plain Tex
math.AG/9909037
Titel: Knopen
Author(s): G. van der Geer
Comments: 18 pagina's, ps-file. In: Vacantiecursus, Onbewezen Vermoedens. CWI Syllabus (1999), p. 75-82.
knopen1.ps
Title: Effectivity of Arakelov divisors and the theta divisor of a number field
Author(s): Gerard van der Geer and Rene Schoof
Comments: 19 pages, Plain Tex with 4 figures
math.AG/9802121
Generalizations of Deuring's Mass Formula;
Author(s): G. van der Geer
Comments: 5 pages, ps-file ; abstract of talk given at San-Feliu-de-Guixols 1997.
san-feliu-abstract.ps
Tables of Curves with Many Points
Author(s): G. van der Geer, M. van der Vlugt
Comments: 16 pages, ps-file ; February 17, 2000. Replaces the Tables for numbers of points on curves over finite fields. A special website for the tables is under construction.
tables-mathcomp8.ps
Tables for numbers of points on curves over finite fields
Author(s): G. van der Geer, M. van der Vlugt
Comments: 23 pages, ps-file ; final (!) update March 19, 1998; See Tables of Curves with Many Points.
tables-Nqg-5.ps
Title: Constructing curves with many points by solving linear equations
Author(s): Gerard van der Geer and Marcel van der Vlugt
Comments: 6 pages, Plain Tex
alg-geom/9711010
Title: Generalized Reed-Muller codes and curves with many points
Author(s): Gerard van der Geer and Marcel van der Vlugt
Comments: 11 pages, Plain Tex
alg-geom/9710016
Title: Knoten
Author(s): Gerard van der Geer
Comments: General audience lecture; 13 pages, ps-file
brocker3.ps
Title: The Chow Ring of the Moduli Space of Abelian Threefolds
Author(s): Gerard van der Geer
Comments: 17 pages, Plain Tex, in: J. of Alg. Geometry 7 (1998).
alg-geom/9702009
Title: Cycles on the Moduli Space of Abelian Varieties
Author(s): Gerard van der Geer
Comments: 22 pages, ps-file
In:Moduli of Curves and Abelian Varieties (The Dutch Intercity Seminar on Moduli), p. 65-89 (Carel Faber and Eduard Looijenga, editors), Aspects of Mathematics, Vieweg, Wiesbaden 1999. main.ps
Title: Generalized Hamming Weights of Codes and Curves over Finite Fields with Many Points
Author(s): Gerard van der Geer, Marcel van der Vlugt
Israel Math. Conf. Proc. 9(1996), 417-432
Title: Quadratic Forms, Generalized Hamming Weights of Codes and Curves with Many Points
Author(s): Gerard van der Geer, Marcel van der Vlugt
Journal of Number Theory 59 (1996), 20-36
alg-geom/9412011
Title: On the existence of supersingular curves of given genus
Author(s): Gerard van der Geer, Marcel van der Vlugt
Journal fuer die reine und angewandte Mathematik 458 (1995), 53-61
alg-geom/9404007
Title: How to construct curves over finite fields with many points
Author(s): G. van der Geer, M. van der Vlugt
Comments: 21 pages, Plain Tex
alg-geom/9511005