Publications of Carel Faber

Preprints

• Polynomial point counts and odd cohomology vanishing on moduli spaces of stable curves
  With J. Bergström and S. Payne. Accepted for publication in the Annals of Mathematics.
  arXiv:2206.07759

Articles

• Cohomology of moduli spaces via a result of Chenevier and Lannes
  With J. Bergström.
  Épijournal de Géométrie Algébrique 7 (2023).
  arXiv:2207.05130

• The S_n-equivariant top weight Euler characteristic of M_{g,n}
  With M. Chan, S. Galatius, and S. Payne.
  Amer. J. Math. 145 (2023), no. 5, 1549-1585.
  arXiv:1904.06367

• Concomitants of Ternary Quartics and Vector-valued Siegel and Teichmüller Modular Forms of Genus Three
  With F. Cléry and G. van der Geer.
  Selecta Math. (N.S.) 26 (2020), no. 4, 55.
  arXiv:1908.04248

• Covariants of binary sextics and modular forms of degree 2 with character
  With F. Cléry and G. van der Geer.
  Math. Comp. 88 (2019), no. 319, 2423-2441.
  arXiv:1803.05624

• Covariants of binary sextics and vector-valued Siegel modular forms of genus two
  With F. Cléry and G. van der Geer.
  Math. Ann. 369 (2017), no. 3--4, 1649--1669.
  arXiv:1606.07014

• The class of the bielliptic locus in genus 3
  With N. Pagani.
  IMRN 2015, no. 12, 3943--3961.
  arXiv:1206.4301

• Siegel modular forms of degree three and the cohomology of local systems
  With J. Bergström and G. van der Geer.
  Selecta Math. (N.S.) 20 (2014), no. 1, 83--124.
  arXiv:1108.3731

• Tautological algebras of moduli spaces of curves
  Moduli Spaces of Riemann Surfaces, 195--217,
  IAS/Park City Mathematics Series, Volume 20, 2013.

• Modular forms and the cohomology of moduli spaces
  Automorphic forms and automorphic L-functions,
  Surikaisekikenkyusho Kokyuroku 1826 (2013), 129--137.

• Tautological and non-tautological cohomology of the moduli space of curves
  With R. Pandharipande.
  Handbook of Moduli (G. Farkas and I. Morrison, eds.), Volume I, 293--330, Advanced Lectures in Mathematics, International Press, Boston, 2013.
  arXiv:1101.5489

• A remark on a conjecture of Hain and Looijenga
  Ann. Inst. Fourier (Grenoble) 61 (2011), no. 7, 2745--2750.
  arXiv:0812.3631

• Tautological relations and the r-spin Witten conjecture
  With S. Shadrin and D. Zvonkine.
  Ann. Sci. École Norm. Sup. 43 (2010), no. 4, 621--658.
  arXiv:math/0612510

• Limits of PGL(3)-translates of plane curves, II
  With P. Aluffi.
  J. Pure Appl. Algebra 214 (2010), 548--564.
  arXiv:0706.1304

• Limits of PGL(3)-translates of plane curves, I
  With P. Aluffi.
  J. Pure Appl. Algebra 214 (2010), 526--547.
  arXiv:0706.1301

• Siegel modular forms of genus 2 and level 2: cohomological computations and conjectures
  With J. Bergström and G. van der Geer.
  Int. Math. Res. Not. 2008 (2008), Art. ID rnn 100, 20 pp.
  arXiv:0803.0917

• On the cusp form motives in genus 1 and level 1
  With C. Consani.
  Moduli Spaces and Arithmetic Geometry (Kyoto, 2004),
  Advanced Studies in Pure Mathematics 45 (2006), 297--314.
  arXiv:math/0504418

• Relative maps and tautological classes
  With R. Pandharipande.
  J. Eur. Math. Soc. 7 (2005), 13--49.
  arXiv:math/0304485

• Complete subvarieties of moduli spaces and the Prym map
  With G. van der Geer.
  J. Reine Angew. Math. 573 (2004), 117--137.
  arXiv:math/0305334

• Sur la cohomologie des systèmes locaux sur les espaces de modules des courbes de genre 2 et des surfaces abéliennes, II
  With G. van der Geer.
  C. R. Acad. Sci. Paris, Ser. I 338 (2004), 467--470.
  arXiv:math/0305094

• Sur la cohomologie des systèmes locaux sur les espaces de modules des courbes de genre 2 et des surfaces abéliennes, I
  With G. van der Geer.
  C. R. Acad. Sci. Paris, Ser. I 338 (2004), 381--384.
  arXiv:math/0305094

• Hodge integrals, partition matrices, and the λ_g conjecture
  With R. Pandharipande.
  Ann. of Math. 157 (2003), 97--124.
  arXiv:math/9908052

• Hodge integrals, tautological classes and Gromov-Witten theory
  Algebraic Geometry and Integrable Systems related to String Theory,
  Surikaisekikenkyusho Kokyuroku 1232 (2001), 78--87.

• Logarithmic series and Hodge integrals in the tautological ring
  With R. Pandharipande. Appendix by D. Zagier.
  Michigan Math. J. 48 (2000), 215--239 (240--252).
  arXiv:math/0002112

• Linear orbits of arbitrary plane curves
  With P. Aluffi.
  Michigan Math. J. 48 (2000), 1--37.
  arXiv:math/9912092

• Plane curves with small linear orbits II
  With P. Aluffi.
  Internat. J. Math. 11 (2000), 591--608.
  arXiv:math/9906131

• Hodge integrals and Gromov-Witten theory
  With R. Pandharipande.
  Invent. math. 139 (2000), 173--199.
  arXiv:math/9810173

• Plane curves with small linear orbits I
  With P. Aluffi.
  Ann. Inst. Fourier (Grenoble) 50 (2000), 151--196.
  arXiv:math/9805020

• Algorithms for computing intersection numbers on moduli spaces of curves, with an application to the class of the locus of Jacobians
  New Trends in Algebraic Geometry (K. Hulek, F. Catanese, C. Peters and M. Reid, eds.),
  Cambridge University Press, 93--109, 1999.
  arXiv:alg-geom/9706006

• A conjectural description of the tautological ring of the moduli space of curves
  Moduli of Curves and Abelian Varieties (The Dutch Intercity Seminar on Moduli) (C. Faber and E. Looijenga, eds.),
  Aspects of Mathematics E 33, 109--129, Vieweg, Wiesbaden 1999.
  arXiv:math/9711218

• Remarks on moduli of curves
  With E. Looijenga.
  Moduli of Curves and Abelian Varieties (The Dutch Intercity Seminar on Moduli) (C. Faber and E. Looijenga, eds.),
  Aspects of Mathematics E 33, 23--45, Vieweg, Wiesbaden 1999.

• Intersection-theoretical computations on M_g
  Parameter spaces; enumerative geometry, algebra and combinatorics (P. Pragacz, ed.),
  Banach Center Publ. 36, 71--81, Warszawa, 1996.
  arXiv:alg-geom/9504005

• A remark on the Chern class of a tensor product
  With P. Aluffi.
  Manuscripta Math. 88 (1995), 85--86.

• Geometric part of Faltings's proof
  Diophantine Approximation and Abelian Varieties (B. Edixhoven and J.-H. Evertse, eds.),
  Lecture Notes in Math. 1566, 83--91, Springer, 1993.

• Linear orbits of d-tuples of points on P¹
  With P. Aluffi.
  J. Reine Angew. Math. 445 (1993), 205--220.
  arXiv:alg-geom/9205005

• Linear orbits of smooth plane curves
  With P. Aluffi.
  J. Algebraic Geom. 2 (1993), 155--184.
  arXiv:alg-geom/9206001

• Chow rings of moduli spaces of curves II: Some results on the Chow ring of M₄
  Ann. of Math. 132 (1990), 421--449.

• Chow rings of moduli spaces of curves I: The Chow ring of M₃
  Ann. of Math. 132 (1990), 331--419.

• Some results on the codimension-two Chow group of the moduli space of curves
  Algebraic Curves and Projective Geometry (E. Ballico and C. Ciliberto, eds.),
  Lecture Notes in Math. 1389 (1989), 66--75, Springer, Berlin.

• Prym varieties of triple cyclic covers
  Math. Z. 199 (1988), no. 1, 61--79.

Unsubmitted

• A non-vanishing result for the tautological ring of M_g
  arXiv:math/9711219

Books edited

• K3 Surfaces and Their Moduli
  With G. Farkas and G. van der Geer.
  Progress in Mathematics 315, ix+399 pages, Birkhäuser, 2016.

• Geometry and Arithmetic
  With G. Farkas and R. de Jong.
  EMS Series of Congress Reports, vii+376 pages, European Mathematical Society, 2012.

• Classification of Algebraic Varieties
  With G. van der Geer and E. Looijenga.
  EMS Series of Congress Reports, viii+338 pages, European Mathematical Society, 2010.

• Moduli of Abelian Varieties
  With G. van der Geer and F. Oort.
  Progress in Mathematics 195, xii+518 pages, Birkhäuser, 2001.

• Moduli of Curves and Abelian Varieties (The Dutch Intercity Seminar on Moduli)
  With E. Looijenga.
  Aspects of Mathematics E 33, viii+200 pages, Vieweg, Wiesbaden 1999.

• The Moduli Space of Curves
  With R. Dijkgraaf and G. van der Geer.
  Progress in Mathematics 129, xii+563 pages, Birkhäuser, 1995.

Thesis

• Chow rings of moduli spaces of curves
  Universiteit van Amsterdam, 155 pages, 1988.