193 citations · 494 across the 27 of their papers we have counts for
13 papers · 1 filter
Motivic Euler characteristics of moduli spaces of curves
Jonas Bergström, Samir Canning, Dan Petersen +1
A combination of recent results of Canning--Larson--Payne--Willwacher and Payne--Willwacher is that the motivic Euler characteristic of the moduli space of nonsingular cu…
Tautological classes with twisted coefficients
Dan Petersen, Mehdi Tavakol, Qizheng Yin
Let be the moduli space of smooth genus curves. We define a notion of Chow groups of with coefficients in a representation of , and we define a subgroup of…
A vanishing result for tautological classes on the moduli of K3 surfaces
Dan Petersen
Looijenga's vanishing theorem on the moduli space of curves says that the tautological ring vanishes above degree . We prove an analogous result for the tautological coh…
Brown's dihedral moduli space and freedom of the gravity operad
Johan Alm, Dan Petersen
Francis Brown introduced a partial compactification of the moduli space . We prove that the gravity cooperad, given by the degree-shifted cohomologies of the s…
The Chow ring of a Fulton-MacPherson compactification
Dan Petersen
We give a short proof of a presentation of the Chow ring of the Fulton-MacPherson compactification of n points on an algebraic variety. The result can be found already in Fulton an…
Poincaré duality of wonderful compactifications and tautological rings
Dan Petersen
Let . Let be the moduli space of -pointed genus curves with rational tails. Let be the -fold fibered power of the universal curve over $M…
The tautological ring of the space of pointed genus two curves of compact type
Dan Petersen
We prove that the tautological ring of , the moduli space of n-pointed genus two curves of compact type, does not have Poincaré duality for any . This resul…
The Gorenstein conjecture fails for the tautological ring of
Dan Petersen, Orsola Tommasi
Let be the smallest integer such that there is a non-tautological cohomology class of even degree on . We remark that there is such a non-tautological c…
The structure of the tautological ring in genus one
Dan Petersen
We prove Getzler's claims about the tautological ring of stable curves of genus one, i.e. that the tautological ring coincides with the even cohomology ring, and that all relations…
On the operad structure of admissible G-covers
Dan Petersen
We describe the modular operad structure on the moduli spaces of pointed stable curves equipped with an admissible -cover. To do this we are forced to introduce the notion of an…
A remark on Getzler's semi-classical approximation
Dan Petersen
Ezra Getzler notes in the proof of the main theorem of "The semi-classical approximation for modular operads" that "A proof of the theorem could no doubt be given using [a combinat…
Cusp form motives and admissible -covers
Dan Petersen
The moduli space of twisted stable maps into the stack carries a natural -action and so its cohomology may be decomposed into irreducible -representations.…
Cohomology of local systems on loci of d-elliptic abelian surfaces
Dan Petersen
We consider the loci of d-elliptic curves in , and corresponding loci of d-elliptic surfaces in . We show how a description of these loci as quotients of a product of mod…