160 citations · 329 across the 26 of their papers we have counts for
26 papers · 1 filter
Cohomology of moduli spaces via a result of Chenevier and Lannes
Jonas Bergström, Carel Faber
We use a classification result of Chenevier and Lannes for algebraic automorphic representations together with a conjectural correspondence with -adic absolute Galois represe…
Polynomial point counts and odd cohomology vanishing on moduli spaces of stable curves
Jonas Bergström, Carel Faber, Sam Payne
We compute the number of F_q-points on M_{4,n}, for n less than or equal to 3, and show that it is a polynomial in q, using a sieve based on Hasse-Weil zeta functions. As an applic…
Concomitants of Ternary Quartics and Vector-valued Siegel and Teichmüller Modular Forms of Genus Three
Fabien Cléry, Carel Faber, Gerard van der Geer
We show how one can use the representation theory of ternary quartics to construct all vector-valued Siegel modular forms and Teichmüller modular forms of degree 3. The relation be…
The -equivariant top weight Euler characteristic of
Melody Chan, Carel Faber, Soren Galatius +1
We prove a formula, conjectured by Zagier, for the -equivariant Euler characteristic of the top weight cohomology of .
Covariants of binary sextics and modular forms of degree 2 with character
Fabien Cléry, Carel Faber, Gerard van der Geer
We use covariants of binary sextics to describe the structure of modules of scalar-valued or vector-valued Siegel modular forms of degree 2 with character, over the ring of scalar-…
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…
The class of the bielliptic locus in genus 3
Carel Faber, Nicola Pagani
Let the bielliptic locus be the closure in the moduli space of stable curves of the locus of smooth curves that are double covers of genus 1 curves. In this paper we compute the cl…
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…
Tautological and non-tautological cohomology of the moduli space of curves
C. Faber, R. Pandharipande
After a short exposition of the basic properties of the tautological ring of the moduli space of genus g Deligne-Mumford stable curves with n markings, we explain three methods of…
A remark on a conjecture of Hain and Looijenga
Carel Faber
After recalling the various tautological algebras of the moduli space of curves and some of its partial compactifications and stating several well-known results and conjectures con…
Siegel modular forms of genus 2 and level 2: cohomological computations and conjectures
Jonas Bergström, Carel Faber, Gerard van der Geer
We study the cohomology of certain local systems on moduli spaces of principally polarized abelian surfaces with a level 2 structure. The trace of Frobenius on the alternating sum…
Limits of PGL(3)-translates of plane curves, II
Paolo Aluffi, Carel Faber
Every complex plane curve C determines a subscheme S of the of 3x3 matrices, whose projective normal cone (PNC) captures subtle invariants of C. In "Limits of PGL(3)-translat…
Limits of PGL(3)-translates of plane curves, I
Paolo Aluffi, Carel Faber
We classify all possible limits of families of translates of a fixed, arbitrary complex plane curve. We do this by giving a set-theoretic description of the projective normal cone…
Tautological relations and the r-spin Witten conjecture
Carel Faber, Sergey Shadrin, Dimitri Zvonkine
In a series of two preprints, Y.-P. Lee studied relations satisfied by all formal Gromov-Witten potentials, as defined by A. Givental. He called them "universal relations" and stud…
On the cusp form motives in genus 1 and level 1
C. Consani, C. Faber
We prove that the moduli space of stable n-pointed curves of genus one and the projector associated to the alternating representation of the symmetric group on n letters define (fo…
Limits of translates of plane curves -- on a paper of Aldo Ghizzetti
Paolo Aluffi, Carel Faber
We study the limits of PGL(3) translates of an arbitrary plane curve, giving a description of all possible limits of a given curve and computing the multiplicities of corresponding…
Complete subvarieties of moduli spaces and the Prym map
Carel Faber, Gerard van der Geer
We prove that in characteristic p>0 the locus of stable curves of p-rank at most f is pure of codimension g-f in the moduli space of stable curves. Then we consider the Prym map an…
Relative maps and tautological classes
C. Faber, R. Pandharipande
The moduli space of stable relative maps to the projective line combines features of stable maps and admissible covers. We prove all standard Gromov-Witten classes on these moduli…
Logarithmic series and Hodge integrals in the tautological ring (with an appendix by D. Zagier)
C. Faber, R. Pandharipande
We describe a new perspective on the intersection theory of the moduli space of curves involving both Virasoro constraints and Gorenstein conditions. The main result of the paper i…
Linear orbits of arbitrary plane curves
Paolo Aluffi, Carel Faber
The `linear orbit' of a plane curve of degree is its orbit in under the natural action of $\PGL(3)$. In this paper we obtain an algorithm computing the degree of…
Hodge integrals, partition matrices, and the lambda_g conjecture
C. Faber, R. Pandharipande
We prove a closed formula for integrals of the cotangent line classes against the top Chern class of the Hodge bundle on the moduli space of stable pointed curves. These integrals…
Plane curves with small linear orbits II
Paolo Aluffi, Carel Faber
The `linear orbit' of a plane curve of degree d is its orbit in P^{d(d+3)/2} under the natural action of PGL(3). We classify curves with positive dimensional stabilizer, and we com…
Hodge integrals and Gromov-Witten theory
C. Faber, R. Pandharipande
Integrals of the Chern classes of the Hodge bundle in Gromov-Witten theory are studied. We find a universal system of differential equations which determines the generating functio…
Plane curves with small linear orbits I
Paolo Aluffi, Carel Faber
The `linear orbit' of a plane curve of degree d is its orbit in the projective space of dimension d(d+3)/2 parametrizing such curves under the natural action of PGL(3). In this pap…